There is no information that gives us a hint to where you live, which would be helpful. All houseplants appreciate very bright light - perhaps not direct sun, but very bright light, nonetheless. Most coleus weaken after they bloom. Hormones and decreasing day length can be blamed for that, but pinching helps to keep them from blooming and helps keep them bushy.

There's not enough information in your post to say with any certainty what the problem(s) might be, but if we only consider what the odds suggest, we would look first to the probability of a heavy soil combined with habitual over-watering. A close second in the line-up of suspects would be the contributory effects of low humidity indoors.

It sounds like you're seeing the symptoms of any one of a number of possible fungal infections, often lumped under the general descriptions of 'damping off' disease or 'root rot'.

Al

Just a guess, but it may be you are watering it too much. It went thought a drastic change from outdoors to inside and usually will loose a lot of leaves and get resettled. If you gave it too much water, then it will develop stem/root rot. Let it dry out, even to the extent of loosing all it's leaves. Slowly give it water only when it is extremely dry. It may be too late. Try to save a few stem cuttings and root them in water in a warm bright spot. Change the water every other day. Use old set out water to remove the chlorine.
Best of luck.
Stush

Raven, I second taking Healthy cuttings, rooting in water.
Remove bottom leaves before placing in water. 'Otherwise they'll rot, making water murky,' and cuttings will soften, be useless.

Change water every other day. Tepid water is best, so keep a second, cleaned container filled w/water.

When it's time to change, discard old water, replace with water from the clean container. Don't forget to fill the container so it's available for the next change.

Coleus cuttings root in shade to medium light..no bright/direct.

After roots are 4" plus, transfer to soil or whatever medium you use.

For some reason, Kong Coleus are fussier than other Coleus. But, don't be discouraged.
Good luck, Toni