There are state laws that regulate the time a company needs to hold your position available while you are on disability/sick leave. In California for example it is 12 weeks. After that time they can terminate you even if you continue to be disabled.
Now if your position was altogether eliminated and there was no position to return to at any time that may be different (if the time is shorter than the state allowance for disability leave).
A company cannot terminate you because of your disability but they can terminate your position or hire a new person to fill your position if your leave extends past the time allowed by the state.
You should look at the documents that you received from your employer when you were hired as it should have the answer in there for you.
By the way you will still receive your STD and your LTD should you qualify. You will have to pay the Cobra premiums for your health care but, and this would be in your plan docs, the company will/should/might reimburse you for those premiums should you go on LTD. Again, check your plan documents.
I was terminated while on STD because I was out longer than the 12 weeks and because my position was eliminated. I know how stressful it is, believe me and it doesn't feel right but an employer only has to follow the state guidelines so that is where you have to look.
Best of luck.