Can you respond to a fetchland activation with a Stifle to counter the search ability?

When you activate a fetchland (such as Flooded Strand), its ability is an activated ability that goes on the stack. Because it uses the stack, any player with priority may respond before it resolves — including by casting Stifle, which counters target activated or triggered ability (CR 116.2a, 116.2b).

Stifle counters the fetchland's ability (CR 701.5 — to counter a spell or ability, remove it from the stack). The fetchland itself has already had its cost paid (tapping and paying 1 life), but since the ability is countered, you do not search your library, and the fetchland remains tapped and on the battlefield. The 1 life paid is not refunded, as costs are paid when the ability is activated, not when it resolves (CR 118.12).

It is important to note that the activation cost (tapping the land and paying 1 life) is paid immediately upon activation before anyone receives priority to respond (CR 602.2). So when your opponent responds with Stifle, the costs are already paid; Stifle only stops the effect (the search and sacrifice).

Concrete example: You activate Windswept Heath, tapping it and paying 1 life. Your opponent casts Stifle targeting the ability. Stifle resolves and counters the Heath's ability. You lose 1 life, Windswept Heath remains tapped on the battlefield, and you do not search for a Forest or Plains.

This interaction is a well-known piece of competitive Magic play, particularly in Legacy formats where Stifle is heavily played to disrupt fetchland activations and deny mana development (CR 602.2, 116.2b, 701.5).