Burst. This is the most blatant failsafe to stop infinite combos: a move that lets you break out of a combo. The game Killer Instinct pioneered this concept, but implemented it badly. Guilty Gear perfected it. While you're getting hit by a combo, you can "burst" out of it to knock the opponent away and avoid being hit further. It's your "get out of jail free card," and every character has it.

You can only burst about once per round. The designers surely knew that this mechanic was so powerful that it had to be closely regulated. If it cost super meter to use, there would be some character who's good at generating super meter and would be able to burst too much. Instead, burst has its own meter. It starts full at the beginning of the fight, and using your burst empties the meter entirely. The meter fills up automatically over time, but the only thing that can affect the speed it fills up is how much you're getting hit. If you get hit a lot, you get it back a bit faster. There's no trick to get it back instantly.

Your burst meter does not automatically refill each round, which was a clever decision. If you're at the end of a round and getting hit by a combo, you might very well choose NOT to burst so that you'll still have that ability at the start of next round. You should only burst if you think it will actually help you win the current round. The overall effect is that you don't see bursts every round because often players save it for the next round. The failsafe is there, but it doesn't get used excessively.

Also, a clever opponent will expect the moment you'll burst and they'll voluntarily stop attacking right before that. That makes your burst whiff, so they can punish the recovery of it with an even bigger combo. Even the failsafe itself has a counter.

Guard Meter. Right under your health meter is a little red meter called the guard meter. It starts at 50% full, and naturally tends to wander back to 50% if it gets higher or lower. The more attacks you block, the higher that meter gets. The more attacks you get hit by, the lower that meter gets. The higher the meter is (the more attacks you recently blocked) the less you benefit from the game's normal system of damage scaling. Usually, when you get hit by a combo, each successive hit is "scaled" down in damage more and more. But when your guard meter is high, even an ordinary combo can do massive damage to you because you are not being protected by the usual damage scaling. This is meant to punish overly defensive players.

On the flipside, the lower your guard meter is (meaning you got hit by a lot of attacks in a short period of time), the more damage scaling you benefit from. A very, very long combo will eventually do only one pixel of damage per hit because of this feature. So even if an infinite combo did exist, it would take an incredibly large number of hits to actually kill you and you could probably burst out of it before then.

Furthermore, you receive another even more important protection when your guard meter is low: reduced hitstun. Every time you get hit by a move, you are briefly stuck in a reeling animation where you can't do anything (except burst). This is the basic concept that allows combos to exist at all, since the opponent can often hit you again before your hitstun ends. But in Guilty Gear, the more you get hit, the shorter your guard meter becomes, which then makes your hitstun shorter. So if there exists a combo that is a "loop" of repeated moves, it may be possible to do 3 or 4 repetitions of the loop, but eventually the opponent's hitstun becomes so short that the combo simply stops working. (They'll be able to block at some point.)