Bi-lateral (on both sides) vocal chord paralysis can come from thyroid surgery or from a nodule pressing on the nerve. You have a nerve that runs through the thyroid called the recurrent laryngeal nerve, it controls vocal chord function. If they damage these nerves, you can have paralysis, sometimes it is only temporary, several days, weeks or months. If they totally blow the operation and knick the nerve, or if there is nodule/cancer growth into the nerves that they must cut around, you can have total paralysis, causing permanent hoarseness or even the need for a tracheostomy (breathing hole in the neck) for the rest of your life. THESE ARE NOT USUAL FOR THYROID SURGERY, IT IS VERY RARE. I have had cancer, I had some paralysis before surgery, but I had a great surgeon, and I have no lasting vocal damage. Hope this helps.
I can only assume from your post that you've had thyroid cancer....... I did a quick search of bilateral vocal cord paralysis - just looking at one site, it seems this* may* result from a thyroid surgery... please provide more information, if possible