There is no direct way. TCP/IP communication is almost invariably programs on one machine communicating with programs on a different machine (or perhaps the same machine), there's no trapdoors that directly instruct the kernel to do anything to files. The only exceptions that leap to mind are network filesystem drivers, and given the number of hoops you have to jump through to get NFS going on purpose, having it happen by accident seems sincerely unlikely! Not to say that there may not be brain-dead distros that have open NFS by default -- but when it's off, it's off, and isn't going to be nudged into running just because someone bothers your network enough. Same goes for any other system daemon capable of creating files -- someone with administrator access actually has to turn it on. Or, someone on the inside can run something on an anonymous port if you haven't firewalled that, but it'll have no more access than the user does...

What's more likely to happen is an exploitation of mundane things. A badly written CGI script could be abused to create and/or execute files in /tmp. (For this reasons some web servers have hardened /tmp/ partitions that literally cannot execute any files in them.) Or a limited account with a weak password gets cracked and they just live in that tiny corner of your machine, connecting to a botnet and cracking passwords for it. And so on. They don't have to crack your whole system to use you, and a smart cracker won't interfere with the operations of your system lest you notice.