I have heard JW's pray for the Brothers and Sisters where the preaching work is under ban or where persecution is going on but never for the general population or other Christians who may also be suffering. The difference I see between local Chruch members and the local JW Congragations I've attended is that JW's, to my knowledge, won't rally together on a local level to get support for injustices or aid to Congragation members that are in some sort of trouble.
For example. Locally there was an elderly man (non JW) who went on a photography trip to Mexico with his Teenage Grandson, they both were into photography. They apparently were taking random photos everywhere they stopped. While at a shop in a small village picking up some snacks, they photographed the Mexican girl who was working behind the counter. On their way out of town, the local Police stopped them and accused them of taking illegal photos of minors and threw them in the local jail. The were to be held until they either paid a hefty fine or until a trial could be held and apparently that can take up to a year. The Grandfather was in need of his medications and the local authorities wouldn't allow him any medical treatment. The Grandfather attended a Church here in our area. The local Church members organized a public rally to raise funds to help him and they went to the media and the State Governor and Senator to bring attention to this case and demand help, which they received. The attention this case received from the media and U.S Government officials embarrased/convinced the Mexican officials to let the two travelers go.
If I were in the same situation when I was a JW, I can't imagine the Elders or local congragation members knowing what to do or even feeling the need to come to my aid. The last thing they'd want to do is bring any attention to themselves by going to the media. (mush't kick up a fuss in case it might shed a bad light on the organization). Nor do I think any one of them would organize a public fund raising or even know the process for enlisting the help of the Governor or Senator. They'd probably hesitate to do anything without first running it by Brooklyn and Brooklyn would probably tell them not to get involved. I could be wrong but after being a lifelong JW my sense is you'd be on your own unless this had something to do with the ministry. A prayer is probably all you'd get and it wouldn't be a public one from the platform.