Fence issue with neighbors. Rental home.

[Chester Tan]

looking at the property line it is exactly between the two property. Issue is they have dogs that is ruining the fence which is why I never changed that side of the fence out. Their dogs have digged under and gotten through and in the end it's time to replace. I'm willing to replace it but worried their dogs will ruine it.

Option one would be to replace it and make sure they understand that if they ruine it by their dogs, they will be responsible for repair. Write some kind of agreement?

Option two. Put another fence towards my side and leave the old one but that is a risk of the old fence falling on it and of course their dogs still ruining it. 

Never dealt with this and I have renters in the home and seems like a safety issue now as the panels can fall anytime. Thoughts and advice please?

They say it's not theirs which I just found out today. They have 3 dogs running around.