Can the BTCitcoins of a wallet be stolen just with the public key?

Example: I have 50 BTC in my wallet, any person very far from me asks for I sell them 50 BTC and they say me they need a POF (Prove of founds), so they ask for I send a small amount of btc, (can be 10,000 satoshis) for they check the wallet in blockchain and make sure I have the enough amount to sell.

I ask this because I have heard a wallet can be cleared just to have the public key and with to have sent satoshis previously.

Please let me to know and if is possible, technical examples why can exists the possibility this happens. Or technically why this cannot happend.

Thank you!