This is a terrible idea, Bitcoin is not a good one for emergency funds,
But what if this safety net is intended for future unforeseen circumstances?

I'd chose stablecoins for emergency funds because they aren't volatile ,
But it also prone to collapse and oblivion,like Terra\Luna, which has been very low-volatility lately.

Whats the price there? $0.05?
imagine having $10,000 worth of Bitcoin as emergency fund and when a new emergency arrives you sold the whole bag for $6000.
But the situation could just as easily be the exact opposite, couldn't it? It depends on which cycle of unforeseen circumstances you happen to land in.
Tell me how this is not possible, Bitcoin have dumped like this few times already, it's best used for long term investment rather than something that's suitable for stable currency.
Moreover, it will demonstrate it. At various times.
Fiat and stable coins are best for emergency funds, anything straight into the future is where Bitcoin should always come in.
The only advantage of fiat and stablecoins is high liquidity. However, there are some doubts regarding stablecoins, as regulators in certain countries are beginning to tighten controls on their circulation; this implies potential liquidity issues (or risks) associated with it.
You mentioned the example of keeping $10k. for unforeseen circumstances. If hold that amount in fiat for years waiting for contingencies that might never actually occur, the money simply loses value. A sensible approach might be to lower that sum, say, to $12k. (minimizing inflation-related losses) and keep the rest in an interest-bearing bank account (while Im not a fan of this, its the lesser of two evils here) that allows for full withdrawal at any time if needed (though this usually results in a lower interest rate).
Therefore, the idea of holding bitcoin as a reserve fund seems neither particularly good nor particularly bad at first glance; it all depends on the circumstances. If its a long-standing investment, any drop in the asset's value is offset by the profits generated from the early entry and the time elapsed since then.
As an alternative solution: what about borrowing money, say, taking out a bank loan, in the event of an unforeseen circumstance (which might not even arise)? Could then make monthly repayments using funds from selling bitcoin. This creates a DCA-like effect, but in reverse, allowing to average out the price of bitcoin being sold to cover the debt. As a result, you won't have to sell a large amount of bitcoin at a loss all at once, and this will offset the losses incurred during a sharp drop in the price of bitcoin. What do you think of this option?