Unpatched software poses no risk by themselves. They're only problematic when someone exploits it.
How could malware get into my system if I do have unpatched software in general and I'm connected to an infected network,
but none of my ports are open except for that very one HTTP port which I use to browse the internet using a secure up-to-date fully-patched drive-by-download-immune text-only browser?
I don't do self-injury by downloading anything. The only one thing I download is if there is a patch for my browser and I would verify the file's checksum multiple times before running it. The checksum is itself obtained via HTTPS/TLS from multiple trustable sources.
Assuming the text-only browser I use is has no security vulnerabilities, how could malware enter my system?