This happens every now and then. It can be a package of fresh mozzarella, or a jar of marmelade, or something else. The packaging used to be flat, now it is plump.
Is this a sign of spoilage or not? How can I tell?
When your packaging has inflated over time, this is always a sign of bacterial activity. The bacteria start multiplying, and produce gases as a waste product, so your airtight packaging acts like a balloon. The pressure can get enough to bulge jar lids too.
For most foods, this is a clear sign of spoilage. You don't want bacteria in your food, especially in canned food! So, discard the food to which it has happened.
The major exception are fermented foods. They are supposed to have a thriving colony of known harmless bacteria in them. When the colony gets larger than you planned, it can inflate the packaging. Nowadays, it is unlikely to see it with storebought food, since they control the bacterial population, but it can still happen e.g. if you leave yogurt in a warm room for a long time, and of course food you have fermented yourself can do it frquently, if you keep it in a closed container. Fermented food is safe after bulging, but you have to check if you still like the taste, which will become quite sharp after overfermentation.
Also, this only applies to foods which changed their volume over time. Potato chips (crisps) are sold in already-inflated bags, but this is not a sign of trouble, it was done in the factory.
If you have no good reason to know that the bulging was caused by a safe process (overfermentation of fermented food, or factory-plump packaging), this is a sign of spoilage. The food is unsafe, no matter if other signs of spoilage are present, or if the typical storage conditions were present.