Ok I will try to help you the best I can. it sounds like to me like you did everything right. although tulips to like cool temps in the 40s but not below freezing so maybe leaving them by the winter is a good idea, as long as you know it will not fall below freezing. Now about the wilting part, it sounds like your bulbs are starting to go dormant for the season, before you think about doing anything with them let me say this,Your right about the tulips being forced any tulips you get this time of year are forced. Forcing them takes a lot out of the tulip bulb which means the chance of them flowering again are not too good Sorry to say this! But if you want to try here is what you do. keep the pot in the sun above freezing temps so the leaves and start to build up strength for next year wait until the leaves have totally dried up keep it moist during this time. after that you can take them out of the pot and store them until fall. and in the fall you should give the tulips 6 to 8 weeks of cool temps in the upper 30s to very low 40s then they Might bloom the next year! but the chances are you will just get leaves with no flowers. but you can always try!

I forgot the mention that tulip bulbs can take below freezing temps, but not the full grown foliage. here in Wisconsin tulips stay in the ground when temps fall below zero, here tulips come back year after year and bloom.

Potted tulips (indoors) only bloom for a week or two at the most. What you are describing sounds like natural decay after flowering is done. Doesn't sound like you did anything wrong.

To enjoy longer indoors potted bulbs should be purchased when still green rather than in full color. Unfortunately, most won't buy them green so most don't sell them green either. They don't make much of a show when given for a gift when green.

Warm indoor temps/sun just encourage them to bloom out faster.

Bulbs have a cycle they go thru. They need dormacy,(no light,water or food) when they "wake up" they will send out roots, then foliage and lastly a flower. The flower is the last stage for bulbs. When the flower fully opens, it only lasts a few weeks. Then the bulb needs to store the energy for the next seasons cycle. It does this in reverse to the growing cycle. The flower dies, the foliage dies (turns yellow, brown then dries out). When this has all happened you an cut off the foliage, quit watering them and put in a cool dark place or if they are in the ground leave them alone and let nature do the rest. This cycle is necessary for the bulbs to store the energy for doing it all over again next year. They only come up and bloom one time per year. Yours are just doing what they are supposed to do. But I agree, since they were forced, they probably won't be good for another season. If you want tulpis outside, buy them in the fall, plant them and wait til spring. (just remeber to plant them, not like me and forget about them til now)