How does gradual crossing over of the Roche limit transform a planet or moon?
A large moon (the size of a planet) would be modeled by the fluid model, meaning friction and tensile strength are too weak to modify the shape of the moon significantly, shape is determined by rotation, vortices, self-gravitation, and tidal forces.
Smaller moons, like Phobos would likely follow a rubble pile model.
On circular orbits tidal heating doesn't play a major role.

The fluid model has been studied extensively. The occuring shapes are known as equilibrium figures.
For a full understanding, the parent body should be considered together with the moons, as one system. (Fluid) moons getting too close to the Roche limit gradually deform (tidal heating depends on inner friction), and start to shed mass at some point. There exist solutions with vortices, and vortex-free solutions, depending on the properties of the fluid. The lost mass may either form an n-body system outside the Roche limit, or form a ring system, mostly inside the Roche limit.
Closer to the planet, it may either impact, and fuse with the planet to a the overall spheroid of the planet, or - if the planet is already rotating fast, and the mass of the moon was sufficiently high - increase the rotation of the planet, such that it may undergo e.g. the Maclaurin - Jacobi series, up to the point, that it cannot accrete more mass. There are several more possibilities in detail.

Rubble piles with tensile strength are more likely to undergo sudden shape changes or disruptions than rubble piles without tensile strength. Behaviour of rubble piles without tensile strength depends on friction. The less friction, the closer to the fluid model.
The more tensile strength of the rubble pile, the more it behaves like the ridgid model. Ridgid objects may survive well below the Roche limit for fluid objects, but disrupt suddenly when tidal forces get too strong.