It doesn't make complete sense. A 'chance stumbling upon' means something you encounter by chance...for example, you might be at the shops and you see something a friend of yours would really love so you decide to buy it and put it away and save it for their Christmas gift.
'A run down' ... It has to be something or someone that is run down. For example, a 'run down house' means it hasn't been maintained for a years and needs a lot of work to make it nice. If a person is feeling 'run down' it means they are lacking in energy and just don't feel that great...generally because they have been very busy / working too much and too hard / stressed etc.
Hope that helps.