If you enter a futures contract, it costs nothing. So every time prices move against you, there is a margin call and you must put up some new money.
Inverse ETF's use a variety of similar strategies to get their returns. Many of these strategies may indeed require a margin call to the ETF issuer if prices move against you. But remember the ETF did not cost nothing. Investors contributed money in order to purchase each share of the ETF. Therefore the ETF issuer has a big pot of money available for use as margin. That's why the margin call never comes through to you.
In a sense, you posted a ton of margin up front, so you won't have to make any additional margin contributions. The money that will be used for margin calls is being kept in treasuries and money market securities by the ETF issuer until it's needed.
If prices move against you badly enough that it looks like the ETF is at risk to not be able to post margin, the ETF would liquidate and you'd get whatever pittance was left after they exit all those positions.