Cat missing for 4 days last seen being chased by a neighbor’s German Shepherd- Advice needed!

I apologize for the very long winded story, but this whole situation caught me off guard and is incredibly complicated. Basically, my mom lives in a manufactured home community with acres of woods behind her. This community has a plethora of stray cats and some had been gathering near her house since she currently has 2 indoor cats. One cat in particular, an older calico that is incredibly sweet and friendly, had been hanging outside for roughly 6 months. My mom would feed her and a few of the other cats but wouldn’t leave the bowl out because of the possibility of attracting another animal. This past Friday, i had plans of scooping her up and taking her to the vet to get checked and once safe, I planned on bringing her home with my 2 other cats. However, Friday morning, my mom noticed the cat was not at her front door like usual. So she checked her door camera and the last footage she had seen of her was her being chased by a neighbor’s German Shepherd at around 8pm. My mom was sleeping at the time and didn’t hear the commotion. When she went to speak to her neighbor about it, it turned out the cat was his and he didn’t seem too upset or concerned. It also turns out that this shepherd is owned by an older couple down the road and he has apparently killed another cat before and they are running the risk of being evicted. We have spoken to other neighbors, put signs up and searched as much as we could (including in the woods which looked to be the direction that she ran last) but haven’t come across anything. We are going on day 4 now and are losing hope. If anyone has tips to find her, or advice in general, I would be forever grateful. We are heartbroken and worried sick. I don’t want to give up hope because we haven’t found any evidence that she could be dead but in the woods there might not be any evidence 😭