It will be marked invalid (unreachable with a hop count of 16), but it will not be removed until the flush (garbage collection) timer expires. The flush timer is 240 seconds, 60 seconds (Cisco routers) after the invalid timer expires the route will be flushed. Those of course are the default timers.
If 180 seconds have already passed then in 60 seconds the route will be deleted. This page is a great resources for in an in-depth explination of RIP timers.
To clarify, with Cisco Routers RIP has 4 timers: update, invalid, holddown, and flush. By default the update timer is 30 seconds, the invalid timer is 6 times the update for 180 seconds, the holddown is also 180 seconds, and the flush timer is 240 seconds.
The invalid timer or what RIP refers to as the expiration or timeout timer, is what determines when a route will be marked unreachable after a period of time (in this case, 180 seconds) of not being updated.
After 180 seconds, the route continues to exist in the route table, and will be advertised as unreachable with a metric of 16. Then after the flush timer expires (60 seconds later), the route wil be removed from the table.
The holddown timer only comes into play when the router receives an update with a higher metric than whats already recorded in its routing table. The router will not accept any new routes for this route unitil the holddown timer expires, then if it doesn't receive an update in 60 seconds when the flush timer expires it will remove the route.
What's interesting is that RIP does not have a holddown timer defined in the RFC, this is a Cisco thing.
So lets say I have 3 routers A, B, and C, connected in the following fashion:
Now C has a route to network 18.104.22.168 and advertises this to B, who in turn advertises this to A. If B does not receive an update from C regarding 22.214.171.124 after 6 updates or 180 seconds, then it marks the route as unreachable and advertises this to A. A, then starts its holddown timer, and the flush timer is reset and starts from zero.
B will advertise the route to 126.96.36.199 as unreachable for 2 more updates or 60 seconds to A, then flush the route.
Since A has the route in holddown, it will ignore those 2 updates, and continue keeping the route in holddown until the holddown timer expires. Then if it does not receive any new updates after 60 seconds, it will also flush the route. Thats a long time from when B decides the route is unreachable, to when A finally flushes the route from its table.
Basically, this takes forever to converge...........so don't use RIP unless you have to, and then make sure you tweak it accordingly.
The route is marked as invalid after the holdown timer expires (180secs).
R 192.168.2.0/24 [120/1] via 10.1.1.2, 00:02:59, FastEthernet0/0R
192.168.2.0/24 is possibly down, routing via 10.1.1.2, FastEthernet0/0
So after that the flash timer starts counting. After the flash timer expires the route is removed from the routing table of the router.
So the answer is 240secs.
The holddown and flush timers start at the same time with invalid timer, but holddown extends till the route is removed from routing table as per the flush timer, so if the route is already marked invalid it will enter extended holddown state i.e. 180 seconds has already passed so the route will be removed from routing table after 240-180=60seconds.