No.
The quantity of addresses is MUCH MUCH TOO BIG for humans to ever use them up. The probability of two humans ever having the same properly generated address in all of human history and future is effectively zero.
What about the bitcoin address collider experiment thing, where they have claimed to find up to 3 different addresses with funds on them? I remember reading about this, but I can't find more details. The website of this thing is:
https://lbc.cryptoguru.org/aboutThey seem to have passed the 1000 trillion mark.
It looks like they're going through private keys counting upwards from 0. Here is an example of a private key, in hex format, that they found to have money on it:
000000000000000000000000000000000000000000000000000022306e3f1a72That private key was probably originally
made to be cracked. Either that or some faulty wallet that made it stored it as a 6-byte integer and it overflowed badly. It was definitely not secure in the first place and our properly generated private keys will never, ever be affected.