No internet connection is needed for homebrew versions.
Many websites claiming to offer a "free Subway Surfers PSP ISO" may contain malicious software or fake files, as the hardware is not natively compatible with the game's engine. Official Alternatives subway surfers psp free
If you absolutely must play on Sony handheld hardware, consider buying a (which has a native port of Subway Surfers available on the PlayStation Store). The Vita can also run PSP homebrew, giving you the best of both worlds. No internet connection is needed for homebrew versions