I've bought a small frozen salmon filet (in a non-vacuum sealed plastic bag) for sushi from a local Japanese market. It took about an hour to get it home via public transit, and the edges had thawed out a bit and became soft by the time I was able to refreeze it. Assuming it was safe to eat when I purchased it, should it still be safe to eat raw now? In general, how long would I have to commute with the salmon unrefrigerated before I should begin to worry about the salmon no longer being safe to eat?
While it is considered safe to refreeze food that has been properly defrosted in a chilled environment, any food that has defrosted in a warm environment (The food temperature danger zone of 40F-140F), should be considered adulterated if it has been left out for too long. The maximum time of 2 hours is applied to food stored between 40F-89F [5C-32C], and 1 hour for food stored above 90F [32C] (USDA danger zone https://www.fsis.usda.gov/wps/portal/fsis/topics/food-safety-education/get-answers/food-safety-fact-sheets/safe-food-handling/danger-zone-40-f-140-f/CT_Index). This is why food should never be defrosted on a countertop.
However, food may be safely refrozen (with a loss of quality) if it still contains ice crystals or is below 40F [5C] (https://www.foodsafety.gov/food-safety-charts/food-safety-during-power-outage).
It is important to note that for any food that is stored in the danger zone, this figure is cumulative. So if your salmon has already spent one hour at between 40F and 89F [5C-32C] during processing and storage etc. prior to freezing, you only effectively have one hour left at that temperature (if defrosted in a refrigerator) before it should be considered unfit to eat.
That is the theory, but in real life it is difficult to ascertain exactly how well food has been stored and treated along the food chain, prior to purchase, unless it is obviously off. Your salmon could be fine, on the other hand, if you had a long journey in hot conditions that lasted over an hour, it might not. Personally, I'd err on the side of caution here and chuck it, as parts of the fillet have probably gone past 40F [5C], especially as you don't intend to cook it. Even then, there is still a level of risk and this is especially pertinent for individuals that are pregnant, have a compromised immune system or are elderly as there are frequently serious complications if people in these categories suffer food poisoning.
Apart from the food safety issues, there is also a matter of quality. Refreezing a partially defrosted salmon fillet will not do it any favours. Depending on how it was initially frozen, a cycle in a domestic freezer will potentially cause damage to the defrosted part.
I would take an insulated cool bag with some ice blocks with you in future if there is any chance of your frozen food defrosting, or that your journey will be an extended time in a hot environment.