A Tower Controller reported an experimental aircraft in the pattern had an engine failure and lost communications and descended below the terrain minimums while returning to the airport to land.

Narrative

Aircraft X was performing an engine break in overhead ZZZ at 1500 ft. He was a bit shaky on the radios and would not always respond. At XA11; Aircraft X requested a descent down to 1000 ft. for landing. I told him unable due to traffic; but then as he crossed overhead the XXR numbers; I told him to descend to 1000 ft. and make right closed traffic for XXR. I received no response. Aircraft Y was inside of a 2 mile final for 28R and Aircraft Y was abeam the numbers on a left downwind for XXL. I attempted to reach out numerous times to Aircraft Y with no response. At XA14 I noticed Aircraft X was low and instructed that aircraft to climb. I then noticed that the target had gone into coast mode on the RADAR. Realizing that Aircraft X had lost communication and likely his engine; I told Aircraft Y to expedite to X and contact Ground. Aircraft X landed on XXR behind Aircraft Y and came to a stop at Taxiway Y.This event was just shocking to me. I hadn't thought of any contingencies in case something like this does happen. I would have expected the pilot to [request priority handling]; or at least advise me of an issue; but having no response; no radar; and then seeing the aircraft very low on a close in downwind; it was unsettling. I hadn't thought this scenario would happen since losing engine and communications is highly unlikely and I recommend I continue to work upon my skills by thinking about contingency plans in case this happens again. I also should have sent Aircraft Y without knowing where Aircraft X was going to end up.