The probe, bereft of an orbiter link and its batteries depleted, will continue to sink deeper into Jupiter's interior. One fate we know the probe won't suffer is to hit a surface, because Jupiter is almost entirely gas. Furthermore, the density of the probe is greater than the density of Jupiter's gaseous interior, and the probe continues to sink after transmissions cease. Thus, what ultimately will destroy the probe is the increasing temperature with depth, which will cause the probe materials to melt and vaporize. Dacron for the parachute, aluminum for the inner equipment shelf and titanium for the outer aeroshell.
Parachute failure causes the probe to drop more rapidly, as shown in the diagram.
Although some interesting chemistry could take place between the molten aluminum and the titanium housing, more likely the aluminum separates from the probe in blobs or droplets, which continue to descend on their own. The probe housing becomes a molten mass, probably breaking up into droplets of titanium that rain down through the dense jovian gas. Where this occurs turns out to be a complicated issue, depending on how much natural titanium and aluminum are in Jupiter's gaseous interior, and what chemical form they're in. To simplify the analysis, we note that evaporation is very slow at low temperatures. However, as the probe continues to fall and the temperature goes up, the evaporation rate increases dramatically.