directly connected routes and OSPF crashes

Hi, I'm just double checking my understanding of OSPF.

When an interface in R1 with OSPF enabled (e.g. "network" statement on IOS) goes down, R1 sends an LS Update and its neighbors remove that route from the routing table. So far so good.

If we enable OSPF on the links between neighbors (say R1-R2, 10.0.0.1/30), that directly connected route will not disappear from R2 until that link is actually down. As that link goes down, the directly connected route disappears from R2, and R2 will update its OSPF neighbors accordingly. As a result, any of R2's neighbors (say R3) will remove the route to 10.0.0.1/30 from their routing tables.

Now, let's say the OSPF process on R1 crashes.

R1 cannot advertise anything. R2 realizes its neighbor is down and will update its neighbors accordingly. Therefore, any route that was previously advertised by R1 gets removed from the routing tables.

However, because the link R1-R2 is still up, R2 will still keep its directly connected route to R1.

In this case, when will R2 stop advertising the directly connected route? I think never, because that link is still up/up, but I'm not sure. Am I right?

Just to be clear, this is not homework (I'm past college...) and I tried finding an answer on RFC2328 but didn't find any (maybe I just missed that?). If there is indeed nothing in the RFC about this, is it a vendor-dependent behavior?