Does canned tuna contain (dead) parasites?

It is quite likely that it does contain them, yes.

A randomly chosen nonpaywalled study of Mediterannean tuna (DOI: 10.14411/fp.2014.011) says that

Overall, 84% of the gills examined harboured metazoan parasites.

Now these are the gills, not the meat in the tin, but it is unlikely that there will be much information on the meat itself:

The research on large tunas is hampered by the high value of fish; therefore, the studies on the use of parasites as tags consider mainly examination of gills, head and viscera, because of their limited (or null) commercial value

I don't know enough about fish parasite to tell you whether the 11 species found are all gill-only, but that sounds unlikely. Where there is an ecological niche, it will be filled. So, extrapolating from the gill parasite numbers to body parasite numbers doesn't sound too bad. And I am pretty certain that the people who prepare the fish don't have any method or reason to go remove the parasites from within the fish meat, just like apple sellers don't have a method to remove the worms from apples. So it sounds entirely believable that there are parasites in most cans of tuna, and if you eat enough of them, your chance of never eating a cooked parasite goes against zero.

Probably only just the "dead" ones, due to the rigors of the canning process -- https://www.quora.com/Does-canned-tuna-have-parasites

TL;DR - Yes, the "monster soup" is pretty much a real thing.

To elaborate, I assume that we are talking about canned food in general, as there's nothing specific about canned tuna except that it's meat, which means it'll definitely go through Pressure Canning

• The industrial canning process is all about Preservation by Sterilization i.e. putting the food in the can, sealing it, ensuring that it's leak proof (air tight) and then heating the under high pressure, high temperature (more than ~ 120°C / 248°F) so that all pathogens and bacteria in it die
• Retort packaging e.g. Capri Sun also undergoes a similar process
• Tetrapac is very similar to retort packaging except it relies on air tight / leak proof packaging and the food is only heat sterilized before packaging (part of the reason why orange juice in such packaging is always devoid of vitamin C)
• As long as the container isn't damaged and within it's expiry date, it should be ideally safe for consumption

If you're concerned about The Dead Parasites

• Yes, some parasites die & remain in the fluid as dead matter and keep floating in Brownian motion (click the link to watch the video)
• Bacteria spores survive canning which remain dormant until the conditions become favorable again i.e. until you open the can (that's why they advise you to consume as soon as possible or refrigerate immediately)

PS:

1. About the criterion you mentioned about quality of tuna / infested with parasites, I guess, that must be regarding the concern for transporting. Tuna fish is too big, too hard to catch & contain, and it is is expensive too. Tuna is usually captured & transported from Japan and if it's already infested with parasites, then it may not survive the journey and the dry ice doesn't help much as the fish is exposed. For the same reasons, some top chefs prefer (small) fishes shipped alive, Tuna fish is too big for that.

2. I became familiar with the Victorian age fantasy word The monster Soup while watching Manu Prakash's Foldscope. The word is a reference to the microbes present in water observed under a microscope.

3. Boiled Dirty Water under the Microscope - This video is cool. I'd definitely recommend watching.

4. In a comment, user: @roetnig has said it correctly - Parasites can be found in any living being (including humans). On the exterior e.g. skin, hair, orifices and even inside the digestive tract. But they are never (or rarely) found in the flesh or blood because the body's defense mechanism gets rid of them. If an animal's flesh or blood contains parasites, then it can mean 2 things: either that animal is suffering from some serious infection or it has been cut open. Most frequently, the latter is the case. Consider it similar to how people get Salmonela, they usually ingest it by consuming contaminated food or water. The doctors surgeons steralize their equipment before the surgery just to prevent the patient dying from bacterial or other parasitic infections.

I bought fresh tuna for my cats today for the first time. It was cut into cubes and packed upon my request. While I was dividing the tuna pieces for freezing, I was disgusted to see white worms in the flesh. Yuck!!!

Apparently, they were in the belly part, embedded in the flesh. I was surprised to find a misleading advice on Livestrong that tuna is an exception to fish carrying parasites. I found at least 10-15 worms in 1 kg tuna. I wish I had clicked a picture to upload.