RAW, they are not still linked once one is dead.
Here's the relevant passage describing the rules for Hag Eyes:
Hag Eye. A hag coven can craft a magic item called a
hag eye, which is made from a real eye coated in varnish
and often fitted to a pendant or other wearable item. The
hag eye is usually entrusted to a minion for safekeeping
and transport. A hag in the coven can take an action to see
what the hag eye sees if the hag eye is on the same plane of
existence. A hag eye has AC 10, 1 hit point, and darkvision
with a radius of 60 feet. If it is destroyed, each coven member
takes 3d10 psychic damage and is blinded for 24 hours.
A hag coven can have only one hag eye at a time, and
creating a new one requires all three members of the coven
to perform a ritual. The ritual takes 1 hour, and the hags can't
perform it while blinded. During the ritual, if the hags take any
action other than performing the ritual, they must start over. (MM p. 176)
So this question can be answered by answering whether the two remaining hags are still in a coven after one dies. It's clear from the text that neither of the effects you asked about applies if there is no coven.
Here's the text describing covens:
A coven consists of three hags so that any arguments
between two hags can be settled by the third. If more than
three hags ever come together, as might happen if two
covens come into conflict, the result is usually chaos. (MM p. 176)
So a coven is three hags. Once one is killed, they are no longer a coven, and the Hag Eye can no longer be seen through by the hags or destroyed to hurt the hags.
Further RAW support
Volo's Guide to Monsters describes the situation you're describing where one of the hags in a coven is killed:
If a member of a coven is killed and the surviving
members intend to keep the group from dissolving,
they immediately attempt to recruit a replacement. This
process involves each prospective member committing
cruel acts with the aim of impressing the remaining
coven members. Adventurers who slay only one member
of a coven might deal a blow to it in the short term,
but later on the surrounding region is wracked with
plaguest curses, and other disasters as the applicants
attempt to outdo one another. (VGTM p. 57-58)
So the surviving two hags try to find a third as soon as possible if they intend to continue the coven - since they cannot do so with just the two of them.