This is also my experience, but people do tend to migrate to a different browser entirely if their workflows don't work in the other browser.

If every website works in Chrome and most websites work in IE, users will switch to Chrome. Same with Safari. If the thing you're building is interesting enough for users to return to it, the unsupported browser may just stop getting used all together, especially if multiple sites break at the same time (i.e. when Safari broke WebAssembly support).