Have you just changed the food Tilly is getting, sometimes it takes a few week for her to get used to it.
Yeah starve her, would work, for a day and let her have her food in smaller portions after, eating too much too fast will make it come out fast too.
When changing food, add a little of the new grub to the old and then over a week make it more and more until she is on only the new grub. Not unheard for pubs to have a diggy tummy for a few days on the trod. As said they will eat anything, our Tilley liked cat poop for a while and was darn fast at getting it down her, only found out when you smelled it on her breath
Of course it it gets worse, time to a visit to the vet with sample poop bag
Does the runny poop look like normal runny poop, as in no blood or creepy crawlies in it?
EDIT good plan there with the neighbour. Rice and chicken is a very good bet and good to solve a sicky pup.