It’s less about grass and more about the underlying soil. If there’s a small layer of topsoil on top of rock, you’re not sinking. If you’re in a low valley with poor drainage and lots of sand and clay, it’s possible. You’d have to look up what various substrates can take in terms of bearing pressure. From there figure out a character’s mass and foot area, find the pressure they’d exert, and you have your answer as to whether they sink.

I’m not a civil engineer so I can’t give you any more details than that, sorry.