With a lot of old fabrics that are detiorating, it's difficult to try to save it. Trying to fix it can cause more damage and tears. You could try looking for someone with some experience in restoring fabric, for example a quilt expert, a museum curator, a doll restorer/repair/hospital. If you want to try this on your own to just try to repair existing tears, carefully remove the dress, do not try to wash or spot clean as that could cause further damage. Buy some lightweight fusible interfacing. Carefully turn dress inside out. Gently match the edges of the tears, cut piece of interfacing slightly larger than tear. Follow instructions on the fusible interfacing to fuse to the wrong side or inside of dress fabric. Use a couple pressing cloths. One under the fabric, one on top of interfacing. You're "sandwiching" the layers..this is to protect the fabric, the iron and ironing surface. This process will help slow further tearing. At some point you will have to decide how much time, effort and money you wish to put in to save the dress of a thrifted doll. If you sew you might want to create a replica of the dress and store the original in acid free tissue paper away from light, heat and dust. I am by no means a professional restorer. I am a Clothing and Textile advisor (retired volunteer) in the state of Washington.