Every person can have unlimited conversations and unlimited messages
in a conversation.
These are two use cases:
Every person can have unlimited conversations
Every conversation can have unlimited messages.
As one of the testing principle is :
Exhaustive testing is not possible .meaning you cannot test all the possibility for a system as the combination ...
unlimited conversations and unlimited messages
something works for an unlimited amount of data, in this case, infinite messages
These two statements may mean different things.
There is no such thing as an infinite number of entities in a computer system because computers have physical limitations, in terms of memory, storage, processing.
What you can do is ...
I see this as a question which should introduce performance / stress tests to determine the number of conversations / messages which still allows user to use the application and number of conversations / messages which the system can actually handle.