What happens when a solid object with a lower density is placed in a liquid with a
greater density?

When the sold object with a lower density is placed on a liquid surface with higher density, the object floats.  Some part of the object is submerged in the liquid and some part is above the surface of liquid.
How much is above the surface of water depends on the densities of the solid and liquid.

The object floats due to the force of buyoyance exerted by the liquid on the solid in the upward direction. This force opposes the force of gravity and balances the sold to be at the top of the liquid surface.