We always compare Bitcoin values in fiat. So in case the fiat system collapses, we may face a collapse for Bitcoin as well. We can't use Bitcoin directly in the current economic system; if we could, then Bitcoin would skyrocket during inflation. Bitcoin has also become a part of the global economy, so if the entire ecosystem collapses, we can't expect something different from Bitcoin as well. So my thoughts are that if we want to make a strong Bitcoin ecosystem, then the global economy must be strong as well.
Some people think that if the fiat system collapses, Bitcoin will become a new great escape, e.g. people will move towards Bitcoin and find hope in it. I think that if the fiat system collapses shortly, Bitcoin will collapse too because we decide its price in USD. When I want to buy a beer and pay with Bitcoin, I pay the USD equivalent of BTC, beer doesn't have a fixed price of 0.0001 BTC for example. If there comes a time when we will start valuing things in Bitcoin alternatively instead of converting USD to BTC at the moment you want to buy things, then we can say that if the fiat system collapses, people might find hope in Bitcoin and stick to it but Bitcoin can't handle large volume of transactions.
Right now, I would say that if fiat collapses, no one will have time to start thinking about Bitcoin because the collapse will cause a disaster in the world.