Can you respond to a fetchland activation with a Stifle to make the player lose a land and life without searching?

When a player activates a fetchland (e.g., Flooded Strand), they pay the costs immediately as part of putting the ability on the stack — this includes sacrificing the fetchland itself and paying 1 life. The ability then goes on the stack and can be responded to (CR 602.2).

Stifle counters target activated ability (CR 700.4, 509.2). When Stifle resolves, the fetchland's ability is countered and has no effect — meaning the player does NOT get to search their library or put a land into play. However, the costs have already been paid and are never refunded (CR 602.2, 117.12). The land is already in the graveyard and the life is already lost.

This is a well-known competitive interaction. The net result is: the fetchland's controller has sacrificed their land, lost 1 life, and gained nothing in return. It is a significant tempo and resource swing.

Example: Your opponent activates Misty Rainforest, sacrificing it and paying 1 life. In response, you cast Stifle targeting the ability. Stifle resolves, countering the search ability. Your opponent is down a land and 1 life with nothing to show for it.

Note that this only works because costs are paid before the ability goes on the stack. You cannot 'undo' a cost payment once an ability is activated (CR 117.12).