TTL is decremented on two occasions:
passing through a router, i.e. being forwarded from one interface to another
delayed in a router queue for certain amount of time, usually one drop in TTL for every second
and is discarded if it turns zero.
Destination host has nothing much to do with that value.
is the "time to live" value also decremented by the receiving host?
No. TTL is decremented before forwarding a packet (RFC 791 states "when it is processed"). When the TTL counter reaches 0 the packet is discarded.
If the destination host would decrement a TTL of 1 to 0, it would need to discard the packet, making all previous transport ...