It won't be an option to use up the accumulated funds before starting afresh to accumulate them if you don't want to risk your bitcoin stash. We should be smart enough to identify those simple mistakes that could endanger years of bitcoin investment in just seconds or few moments.
Then just invest on Bitcoin money that you don’t have special allocation on it so that you will keep your finances normal even if a financial problem arise. As already pointed out by JJG, people frequently invest all their money for the sake of profit even though it’s allocated for something important.
You don’t need to think or consider a backup fund related to your Bitcoin investment if you are just allocating money that has no use on your daily expenses or future expenses.