Unique Rectangle Type 2
When two rescue cells on the same side of a Unique Rectangle each carry the same extra candidate, one of them must hold that digit — and it can be removed from every other cell that sees both rescue cells.
What is Unique Rectangle Type 2?
Type 2 builds on the same deadly-pattern idea as Type 1, but now two corners on the same side of the rectangle each carry one extra candidate — and that extra candidate is the same digit in both cells. The deadly pattern can only be avoided if at least one of those two rescue cells holds the shared extra digit, which means the pair of rescue cells collectively must contain it. That locks the extra digit into the two rescue cells, exactly like a locked pair, and the digit can be scrubbed from any other cell that shares a house with both.
The key difference from Type 1 is that the elimination happens outside the rectangle, not inside it. In Type 1 the deadly pair is removed from the rescue cell itself; in Type 2 the shared extra candidate is removed from the rescue cells' common peers. The rescue cells keep all their candidates — the extra digit is just pinned to them so it cannot appear elsewhere in their shared houses.
How to spot it
Find a rectangle whose four corners all share the same two candidates, then check whether two corners on the same side (same row or same column) each carry exactly one additional candidate — and whether that addition is the same digit in both. If so, that digit is locked into the two rescue cells and can be removed from every cell that sees both of them. The rescue cells must be in the same house for the elimination to reach beyond the rectangle itself, which is guaranteed when they sit on the same side.
The logic
If neither rescue cell held the shared extra digit, both would contain only the deadly pair, and the rectangle would collapse into the deadly pattern — two interchangeable solutions. Because the puzzle has a unique solution, that cannot happen, so at least one rescue cell must contain the extra digit. Whether it is the first or the second, the digit is confined to the pair, and any other candidate for that digit in a house shared by both rescue cells is impossible. The elimination follows from the uniqueness guarantee plus the locked-pair reasoning.