What does a network switch do with frames who's destination MAC address is unknown and is never learned?

I understand the basic switch functionality of flood, forward, filter. When a switch receives a frame with a destination MAC that is not know to the switch it will flood every port (except the receiving port) with the frame in hopes to learn what port the destination address resided on and subsequently enters it into it's mac_address:port table should the destination device respond.

But what happens if the destination device is off or not able to respond to network traffic?

Does the switch continue to flood all ports each time it receives a frame destine for that same address or does the switch start dropping the frames at some point? If it continues to flood ports each time could this be used as a form of dDoS?

Am I right to assume the TCP session layer (3-way handshake) would eventually give up trying to connect after the first SYN packet is sent to the destination address triggering a 'host unreachable' up to Layer-7?