It isn't normal, no. Not entirely sure what the problem is, but there are a couple of observations to make from the images you've posted. First, the soil in the pot is too low, which means the plant gets less light than it should because of the amount of pot sticking up above it. Second, the soil it's in looks like it might be pretty wet, though it's hard to be sure, so I'm wondering if there are drainage holes in the pot. If there are, do you have it standing in a tray or something to catch excess water, and if you do, that should be emptied out 30 minutes after you've watered if any water has collected there. These plants like high humidity and don't like to be in dry soil, but nor will they like being in wet soil that doesn't drain freely. The other possibility is, its going into its dormant period, but as its been like this since you bought it, I'd still recommend the soil level in the pot is corrected. Some further guidance here https://www.carnivorousplants.co.uk/resources/venus-flytrap-complete-guide/
UPDATE following your comment below. If the soil has remained too wet, then what I also suspected may be true - the pot you've used is way too big for the plant. I don't know how long you've had the plant, but if its a relatively recent purchase (in the last 6-8 weeks), then I think you should find another pot which is only about 1, maybe 2 sizes bigger than what it was in when you bought it asap. Despite the fact its about to go into dormancy, I would decant it from its pot and replant into a smaller pot now, at the right height, using fresh potting soil from the carnivorous plant soil you bought, being careful not to damage the roots. Water in lightly, just to dampen the new soil, and see what happens. You were always going to have to decant and repot anyway - you can't raise the soil level with moss or anything else without resituating the plant higher up. And leaving it sitting in lots of wet, unoccupied soil while its dormant won't be doing it any good at all - I think the risk associated with repotting it now into something smaller is a lesser risk than leaving it as it is all winter.