Does a chess position exists where one player has insufficient material, and at the same time has a forced mate in 2?

Question

I was thinking about the USCF and FIDE rules on flagging when the opponent has insufficient material. I think I came up with a scenario with the USCF-rule where the best move would be to let the clock run out. However, I'm unsure if such a position actually exists or not.

Here's the scenario (with USCF rules):

Assume white has insufficient material (KN or KB), but at the same time has a forced mate in 2 due to the placement of black's pieces. After white plays the first move in the forced sequence, black's best move (with USCF rules) would be to let the clock run out because it would be a draw.

Does such a position exist, or is it impossible?

Edit:

A bit more info on the rules I am talking about (in my own words):

According to USCF rules, if a player runs out of time when the opponent has insufficient material, the game is ruled a draw.

According to FIDE rules, if a player runs out of time when the opponent has insufficient material, the game is ruled a loss as long as there exists a legal sequence of moves that leads to check mate.

Answer 1

After white plays the first move in the forced sequence, black's best move (with USCF rules) would be to let the clock run out because it would be a draw.

No, it wouldn't be a draw if there was a forced mate and the losing side ran the clock out. Under USCF rule 14E:

The game is drawn even when a player exceeds the time limit if one of the following conditions exists as of the most recently determined legal move:

14E2. King and bishop or king and knight. Opponent has only king and bishop or king and knight, and does not have a forced win.

Since in your scenario the opponent does have a forced win, this does not apply, and the side that runs the clock down will lose.

Answer 2

You have misunderstood the rules. What you describe is incompatible with the FIDE Laws of Chess. There is no concept of "insufficient material". This is what they say:

5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7

Basically to be a draw under this rule helpmate has to be impossible.

The wording in the latest version of the USCF rules that I have seen is badly worded and may have helped cause your confusion but basically amounts to the same thing:

14D. Insufficient material to continue.

The game is drawn when one of the following endings exists as of the most recently determined legal move, in which the possibility of a win is excluded for either side

Thus K+N vs K is drawn as is K+B vs K but K+N vs K+B is not. Either side can still win.