EDIT: After more research apparently (although it is not explicitly stated) they only issue USDT per USD they receive. And vice-versa. So they can exchange as much BTC for USDT as they want, and can take a gain or loss on it, but it should not affect the reserves, thus they should be able to maintain solvency. They are not/do not have a bank, but store the USD in external commercial banks, so the funds should be relatively well-protected. There is always the risk that the company absconds with the money. Tether is incorporated in the Virgin Islands. There is some concern that the founder, Brock Pierce, was involved in a child sexual abuse ring:
https://www.buzzfeed.com/hunterschwarz/mystery-man-at-center-of-alleged-hollywood-sex-ring-has-vani