Two aspects.
BA and IB are one company; i.e. IAG. If BA and/or IB went under, there will be no ability to spend Avios wherever you left them. The question is whether one airline could collapse but not the other airline. Never say this will never happen given the precedent with airlines in the US as we have Air Europa as something to point to. Having said that, Avios does let you redeem on non-BA/IB flights where they buy the tickets. I recall another post where the airline did not know that Avios were selling their flights. However, the Avios business model would be severely weakened.

If the concern is about BA freezing your Avios with the account being under audit, then Avios would be the safer place to store them since I doubt if BA could freeze your Avios account. There are instances where Avios has "bought tickets" either on BA or non-BA/IB flights.

In theory , the should not be able to freeze your IB account but who knows what BA is able to do.