Friction fit connectors slightly opened

First off, can you add a picture of the connector to your question so we can see which connector it is and what shape it's in? From that we may be able to determine whether resoldering or replacing are viable options, as well as whatever else we can think of to fix it.

My first thought would be that most of those friction fit connectors are one-sided, meaning there are only connections on one side of the flex cable, not both. In that case, it may be possible to take a piece of thin plastic cut to the same width as the ribbon cable and slide it in along with the flex cable in order to add thickness to it to compensate for the widened opening. You'll probably have to experiment with various material thicknesses to get the right balance between being too thick to insert and too thin to make good contact. I'd strongly suggest you stick to non-conductive materials as much as humanly possible.