What happens to your savings if a recession or depression hits?

For example if I have 5k in a traditional or online savings/checking account will I have access to this money when I need it?…in the midst of a depression for example? Or at that point does my money temporarily "vanish" I know that it is insured but Im talking about the accessibility. Also what happens to the dollar during that time is it’s value lower or higher? Any help would be great. Thanks!