Can you use a fetchland to search for a land while you are at zero life?

You can absolutely activate a fetchland (such as Flooded Strand) even when you are at 1 life — or even 0 life in some edge cases — because activating an ability only requires you to pay its costs and put it on the stack. Nothing prevents a player at 0 life from taking game actions in the middle of resolving something.

The critical point is when state-based actions are checked. Under CR 704.3, state-based actions are checked whenever a player would receive priority — not continuously during resolution. So when the fetchland's ability resolves, you search your library, put the land onto the battlefield, then the ability finishes resolving. Only after the ability is completely done does the game check state-based actions.

If paying the fetchland's 1 life cost drops you to 0 (or below), CR 704.5a states that a player with 0 or less life loses the game. This check happens after the ability resolves, so the land does enter the battlefield — but you immediately lose the game before you can do anything else with it.

Concrete example: You're at 1 life and activate Windswept Heath. You pay 1 life (dropping to 0), search for a Forest, and put it onto the battlefield. The ability finishes resolving. The game then checks state-based actions, sees you're at 0 life, and you lose. The Forest entered play, but it doesn't matter.

Note: If you are somehow already at 0 life (e.g., held there by a replacement effect like Platinum Angel), you can still activate the fetchland, but paying 1 life puts you to -1, and you will lose once state-based actions are checked after resolution (CR 704.5a).