What happens to a VTP client if it can't locate a VTP server? Also what happens after the client reboots and can't locate a server?
When speaking about all recent IOS-based Catalyst switches, in both cases, the VTP Client will simply run with its locally stored vlan.dat file and its current contents. The net result is that the VTP Client will work as it did before the reboot, assuming no change to the VTP domain has occured in the meantime.
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As Peter notes, client device will use its own copy of the VLAN database. However, you wouldn't want to leave this uncorrected as this client can now be different from the "server's" VLAN database and/or a "client" might distribute its VLAN database to other clients. (Often not realized, "clients" share their VLAN database too.)