Do rich people never have to pay back what they borrow with their wealth as security? Does the same apply in my case?

Obviously, no one here is going to know exactly how some rich person or another manages their finances.

In general, however, if someone owns a property, they can take out a loan against that property. Either a line of credit that the property owner can take money from whenever they want up to some limit or a lump sum. It is certainly conceivable that the bank would allow the property owner to simply let the interest accrue on the line of credit or to structure the loan so that no monthly payments are due but the entire loan must be repaid in, say, a year with the expectation that the wealthy person will take out a new loan in a year to repay the old loan with interest. Assuming that the property appreciates faster than the rate of interest + any additional spending, the person could conceivably live on loans permanently.

As a practical matter, however, there are going to be several hurdles to doing the same thing with a bitcoin fortune

• There is an existing, very well understood process by which banks put a lien on a property when they make a loan against it which ensures that the property can't be sold until the bank is paid back. This makes real estate loans much less risky and lets the bank charge much less interest.
• Banks are comfortable that real property is going to hold its value or increase in value over time. Sure, you'll have dips like we saw in 2008 and local areas might experience downturns but real estate has a pretty long history of growing in value. If a bank loans out, say, 80% of the value of the property, the odds that the price drops 20% and leaves the loan underwater are pretty low.
• There are enough people that want to put up real property as collateral for a loan that the banks can diversify their risk by lending to lots of different people with lots of different properties in lots of different areas. The odds that a single property drops in value by 20% are low but if the bank has lots of different loans against a variety of different properties, it can weather the inevitable cases where individual properties drop in value. This also allows them to develop and standardize processes for creating loan products, underwriting, selling assets to investors, etc.
• Wealthy people have other assets than the property. So the bank knows that even if the property drops in value, the borrowers could sell something else to pay back the loan.

Trying to get a loan against your bitcoin will be much harder

• Banks don't have an easy way to put a lien on your bitcoin to ensure you can't sell it until you've satisfied the loan. They also don't have a way to insure that you don't lose your bitcoin somehow (hackers, lost password, etc) If someone was going to lend against bitcoin, I'd expect that they'd require you to send the coins to their wallet before they sent you the money. And they would probably have the ability to liquidate your coins if they dropped in value unless you put up additional collateral.
• Bitcoin does not have a history of holding its value. Rather, it is an incredibly volatile asset that can easily drop 20% in a day. If someone was going to lend out money with bitcoin as collateral, they'd need to lend out far, far less of the value of the coin to be as safe as loaning out 80% of the value of a property.
• Lending against bitcoin and other cryptocurrencies does little for diversification. If a bank makes dozens of bitcoin loans to dozens of borrowers, it doesn't reduce its risk at all-- if one person's bitcoin drops in value, so will everyone else's. It also isn't common enough that banks would be likely to have standardized processes for underwriting, selling assets to investors, etc. which means that you'd be looking at a relatively expensive loan to originate and hold.
• You may or may not have other assets that the bank expects you'd be able to sell to pay back the loan in the event that your bitcoins dropped in value.

While it is certainly conceivable that someone somewhere is going to be willing to loan you money against bitcoin collateral, it is likely that such a loan will be relatively expensive in terms of fees and in terms of interest rate and that it will loan out a relatively small fraction of your coin's value. And it is probably not something that the local branch of Banking Megacorp is going to have a brochure on.