It’s a little tricky to understand what is meant by information. It is fundamental to quantum mechanics that future states of a quantum system are determined from past states of quantum systems. So, if initially, we have a complete as possible description of a quantum system, all future states of the quantum system must be traceable back to that initial description. We can’t ‘lose’ possible future states nor can we gain possible states that can’t be traced back to the space/time evolution of the original system. Note this doesn’t invalidate the notion of probabilistic measurement of a particular state - it means whatever states are available have to be traceable to past states.
So, back to black holes. We cannot lose that traceability to the past when a black hole radiates since the original conception of Hawking radiation was that it was completely random. This is the information paradox. The belief now is that the information is preserved at the event horizon and is entangled in emitted Hawking radiation.
Unfortunately, that has led to the recent ‘firewall problem’. The information entangled in the Hawking radiation is maximally entangled - virtual particle pairs where one passes into the event horizon and the other doesn’t - cannot also be entangled. This requires that entanglement to be broken between virtual pairs, releasing massive energy at the event horizon. This conflicts with general relativity.
So, the bottom line is this is still a heavy area of research. Lot of ideas, but we cannot consider the issue solved.