It varies with the studio. The most common ways I've seen for studios to stay running between releases are:
Take out loans. The studio borrows money, only pays the interest/minimum payment, and uses the rest to pay for development in hopes of paying the loans off when the game releases.
Sell a stake in the studio. Investors may wish to buy a piece of a studio in hopes that it will become more valuable once the game releases. The studio can then use that money to pay for development. The stake being sold can be anything from a minority share up to the entire studio.
Do a "day job" to pay the bills. Several studios will do contract work for other companies to pay the bills and fund the development of their own projects. As an example, Behaviour Interactive developed Dead by Daylight but also does a lot of freelance work for other publishers contracting jobs like porting games to other platforms.
Have an alternate source of revenue. Valve has Steam, CDPR has GOG, Epic has the EGS and Unreal Engine, and so on. Some places have additional sources of income beyond the game releases.
Crowdfund. Some studios turn to the public to get themselves over that hump.
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