This is possible, but not exactly in the way you’re expecting!
Consider what you really want here: is it just an increased number of dollars or BTC? Nope! What you want is an increase in your buying power. Stop to think about the difference here for a second – it is important!
The goal is an increase in buying power, which means you want the ability to buy more tomorrow, than you could today.
Banks pay interest on deposits because they will use those deposits to make investments of their own, and those investments will (hopefully) do well and make the bank some profits. The actual cash money itself doesn’t just magically grow! In fact, the opposite is true: as the money supply grows (unpredictably!), each individual dollar will hold less buying power than it did before. So just keeping dollars stored under a mattress is actually a pretty bad idea: that money will have less buying power tomorrow, than it did today. If the goal is to increase buying power, then clearly just holding dollars is bad, and so the prudent individual will find investments that can increase in value over time. With enough money invested, they can ‘live off the interest’ of those investments.
Bitcoin, on the other hand, is a very different type of money, in that the supply of it cannot be inflated, so the act of just holding coins does not suffer from the same issue of unpredictable dilution that dollars do. If BTC maintains current adoption/use rates*, and society progresses and grows in GDP, then each BTC will accrue more buying power over time.
The difference should be obvious: dollars are a bad asset to hold, they lose purchasing power over time due to an (unpredictable) dilution of supply. Bitcoin does not suffer from this, so a holder might expect their purchasing power to increase over time. Many people call bitcoin a ‘hard money’, as in, ‘it is hard to produce more of’.
So all of that is to say: just like dollars, if you hold enough BTC, you could maintain a certain amount of purchasing power over time, while still living off the nominal increase in purchasing power of your BTC. The actual number of BTC you own would slowly shrink, but this is somewhat inconsequential if your goal is to just live off the interest while maintaining your net purchasing power.
*of course, bitcoin is currently in a young stage of growth, so it is a fairly volatile asset in regards to purchasing power over short time frames. But consider what the situation would be if it were as widely adopted as dollars – that is the more interesting situation in regards to the idea I mean to put forth here. Of course, if bitcoin continues to grow in popularity and use, then we might expect the buying power of a coin to increase, and vice versa.