According to this answer and this question the Voyagers will run out of power to "operate a single instrument" in 2025 for Voyager 2 and a little longer for Voyager 1. It is purported to be the end of mission.
But there is scientific data available even from a weak carrier, or from a 40 bit/sec transmission of internal engineering data, even if there are no scientific instruments running.
The Doppler shift provides a continued measure of velocity, and that can potentially provide some information about gravitational potential in the interstellar region. There could even be surprises if a body with some mass passed by and perturbed one of their trajectories slightly.
The frequency, amplitude, and phase of the are also affected by plasma, so if something happened unexpectedly there could be a change. If the spacecraft were bumped by something, the pointing would be altered and this would show up in the strength of the received signal.
So please, no arguments that there is no science to be had once the science packages are turned off!
Suppose there was funding and support to keep listening to the Voyagers as long as they could continue to transmit anything at all, and instructions were sent to configure them in such a way as to allow them to transmit some minimal signal for as absolutely long as possible.
What specifically would be the last straw for the Voyagers that would shut them down or silence them?
Would there be a low-power fault interrupt, or would something burn out, or would the computer's electronics get too cold to operate, or would the radio electronics get too cold to operate, or maybe something else?
Per this answer and references therein, there is plenty of room in the link budget to receive signals from them for a long time to come, much longer than they are likely to last in terms of electrical power.