What will happen when Bitcoin runs out of bitcoin addresses, or is that not possible?
We will run out of humans first.
Even if it happens
It won't.
it is probably possible to fix the problem by using old empty addresses
It isn't.
or by creating new one with a different manner
Unnecessary, for this concern but likely if a weakness is ever discovered in ECDSA, SHA-256, or RIPEMD-160.
Worry more about when we reach the 21 million bitcoins created.
Why?
So that makes 26+26+10 Combination for each step. 27 to 32 letters.
Except we don't use 0,O,I, or l so it's more like 24+25+9 with I think equals
58. Then the last few characters of the address are a
checksum to prevent typos resulting in actual addresses. This means they are entirely dependant on the rest of the address and can't change. Perhaps that's why it's called
Base58Check encoding.
Try 32^56 adresses.
I've been known to make a mistake on this, but I think you've got your base and your exponent switched there.
Maybe it stops working in 2200 when we are 2 Trillion humans
More likely we'll still have plenty of addresses 4 billion years from now (assuming of course humans still exist and we are still using something as ancient and old fashioned as bitcoin).