[MC-135550] Full filesystem caused major server issue

The server had its filesystem full and now there is a problem printed in the log and also my user cannot connect. The log file "latest.log" is attached.
1.13: latest.log
[00:36:56] [main/WARN]: Ambiguity between arguments [teleport, destination] and [teleport, targets] with inputs: [Player, 0123, @e, dd12be42-52a9-4a91-a8a1-11c01849e498]
[00:36:56] [main/WARN]: Ambiguity between arguments [teleport, location] and [teleport, destination] with inputs: [0.1 -0.5 .9, 0 0 0]
[00:36:56] [main/WARN]: Ambiguity between arguments [teleport, location] and [teleport, targets] with inputs: [0.1 -0.5 .9, 0 0 0]
[00:36:56] [main/WARN]: Ambiguity between arguments [teleport, targets] and [teleport, destination] with inputs: [Player, 0123, dd12be42-52a9-4a91-a8a1-11c01849e498]
[00:36:56] [main/WARN]: Ambiguity between arguments [teleport, targets, location] and [teleport, targets, destination] with inputs: [0.1 -0.5 .9, 0 0 0]
[00:36:56] [main/INFO]: Loaded 0 recipes
[00:36:56] [main/INFO]: Loaded 0 advancements
[00:36:56] [Server thread/INFO]: Starting minecraft server version 1.13
[00:36:56] [Server thread/INFO]: Loading properties
[00:36:56] [Server thread/INFO]: Default game type: SURVIVAL
[00:36:56] [Server thread/INFO]: Generating keypair
[00:36:56] [Server thread/INFO]: Starting Minecraft server on *:25565
[00:36:56] [Server thread/INFO]: Using epoll channel type
[00:36:57] [Server thread/INFO]: Preparing level "world"
[00:36:57] [Server thread/INFO]: Reloading ResourceManager: Default
[00:36:59] [Server thread/INFO]: Loaded 524 recipes
[00:37:00] [Server thread/INFO]: Loaded 571 advancements
[00:37:00] [Server thread/ERROR]: Error loading saved data: villages
java.io.EOFException: null
	at java.util.zip.GZIPInputStream.readUByte(GZIPInputStream.java:268) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.readUShort(GZIPInputStream.java:258) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.readHeader(GZIPInputStream.java:164) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.<init>(GZIPInputStream.java:79) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.<init>(GZIPInputStream.java:91) ~[?:1.8.0_181]
	at hi.a(SourceFile:25) ~[server.jar:?]
	at cbz.a(SourceFile:66) ~[server.jar:?]
	at cbz.a(SourceFile:51) [server.jar:?]
	at tc.b(SourceFile:142) [server.jar:?]
	at net.minecraft.server.MinecraftServer.a(SourceFile:351) [server.jar:?]
	at sn.d(SourceFile:248) [server.jar:?]
	at net.minecraft.server.MinecraftServer.run(SourceFile:541) [server.jar:?]
	at java.lang.Thread.run(Thread.java:748) [?:1.8.0_181]
[00:37:00] [Server thread/ERROR]: Error loading saved data: villages_nether
java.io.EOFException: null
	at java.util.zip.GZIPInputStream.readUByte(GZIPInputStream.java:268) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.readUShort(GZIPInputStream.java:258) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.readHeader(GZIPInputStream.java:164) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.<init>(GZIPInputStream.java:79) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.<init>(GZIPInputStream.java:91) ~[?:1.8.0_181]
	at hi.a(SourceFile:25) ~[server.jar:?]
	at cbz.a(SourceFile:66) ~[server.jar:?]
	at cbz.a(SourceFile:51) [server.jar:?]
	at sx.b(SourceFile:69) [server.jar:?]
	at net.minecraft.server.MinecraftServer.a(SourceFile:355) [server.jar:?]
	at sn.d(SourceFile:248) [server.jar:?]
	at net.minecraft.server.MinecraftServer.run(SourceFile:541) [server.jar:?]
	at java.lang.Thread.run(Thread.java:748) [?:1.8.0_181]
[00:37:00] [Server thread/ERROR]: Error loading saved data: villages_end
java.io.EOFException: null
	at java.util.zip.GZIPInputStream.readUByte(GZIPInputStream.java:268) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.readUShort(GZIPInputStream.java:258) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.readHeader(GZIPInputStream.java:164) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.<init>(GZIPInputStream.java:79) ~[?:1.8.0_181]
	at java.util.zip.GZIPInputStream.<init>(GZIPInputStream.java:91) ~[?:1.8.0_181]
	at hi.a(SourceFile:25) ~[server.jar:?]
	at cbz.a(SourceFile:66) ~[server.jar:?]
	at cbz.a(SourceFile:51) [server.jar:?]
	at sx.b(SourceFile:69) [server.jar:?]
	at net.minecraft.server.MinecraftServer.a(SourceFile:355) [server.jar:?]
	at sn.d(SourceFile:248) [server.jar:?]
	at net.minecraft.server.MinecraftServer.run(SourceFile:541) [server.jar:?]
	at java.lang.Thread.run(Thread.java:748) [?:1.8.0_181]
[00:37:00] [Server thread/INFO]: Preparing start region for level 0
[00:37:01] [Server thread/INFO]: Preparing spawn area: 4%
[00:37:02] [Server thread/INFO]: Preparing spawn area: 8%
[00:37:02] [Server thread/INFO]: Preparing spawn area: 12%
[00:37:02] [Server thread/INFO]: Preparing spawn area: 16%
[00:37:03] [Server thread/INFO]: Preparing spawn area: 20%
[00:37:03] [Server thread/INFO]: Preparing spawn area: 24%
[00:37:03] [Server thread/INFO]: Preparing spawn area: 28%
[00:37:04] [Server thread/INFO]: Preparing spawn area: 32%
[00:37:04] [Server thread/INFO]: Preparing spawn area: 36%
[00:37:04] [Server thread/INFO]: Preparing spawn area: 40%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 44%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 48%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 52%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 56%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 60%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 64%
[00:37:05] [Server thread/INFO]: Preparing spawn area: 68%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 72%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 76%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 80%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 84%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 88%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 92%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 96%
[00:37:06] [Server thread/INFO]: Preparing spawn area: 100%
[00:37:06] [Server thread/INFO]: Time elapsed: 6005 ms
[00:37:06] [Server thread/INFO]: Done (9.298s)! For help, type "help"
[00:37:09] [Server thread/WARN]: Can't keep up! Is the server overloaded? Running 2231ms or 44 ticks behind
[00:37:36] [User Authenticator #1/INFO]: UUID of player Boeotian is dbe1c8b1-4e1e-4026-a782-c5e90edfe3b4
[00:37:37] [Server thread/WARN]: Failed to handle packet for /62.1.126.63:53543
java.lang.IllegalStateException: Not a JSON Object: null
	at com.google.gson.JsonElement.getAsJsonObject(JsonElement.java:90) ~[server.jar:?]
	at wn.a(SourceFile:82) ~[server.jar:?]
	at wn.<init>(SourceFile:48) ~[server.jar:?]
	at vo.a(SourceFile:915) ~[server.jar:?]
	at te.<init>(SourceFile:159) ~[server.jar:?]
	at vo.g(SourceFile:442) ~[server.jar:?]
	at ud.b(SourceFile:113) ~[server.jar:?]
	at ud.Y_(SourceFile:65) ~[server.jar:?]
	at hw.a(SourceFile:238) ~[server.jar:?]
	at ua.c(SourceFile:171) [server.jar:?]
	at net.minecraft.server.MinecraftServer.w(SourceFile:749) [server.jar:?]
	at sn.w(SourceFile:357) [server.jar:?]
	at net.minecraft.server.MinecraftServer.v(SourceFile:656) [server.jar:?]
	at net.minecraft.server.MinecraftServer.run(SourceFile:559) [server.jar:?]
	at java.lang.Thread.run(Thread.java:748) [?:1.8.0_181]
[00:37:37] [Server thread/INFO]: com.mojang.authlib.GameProfile@65408ec7[id=dbe1c8b1-4e1e-4026-a782-c5e90edfe3b4,name=Boeotian,properties={textures=[com.mojang.authlib.properties.Property@2015ca41]},legacy=false] (/62.1.126.63:53543) lost connection: Internal server error
[00:37:50] [Server thread/WARN]: Can't keep up! Is the server overloaded? Running 25892ms or 517 ticks behind