Fence Issue: neighbour wants to build a shared fence

Try to work out a payment plan or promise to pay when you can. Don't suggest they put it on their side that will make you a really bad neighbour.

Just remember, if you don't pay, and it's inside their side of the property line, it is their fence, and you can't use it to hang plants, lean tools on it, use the corner post for another section of fence, or any other various things people do with fences. And if they decide to only put the boards on their side and leave you looking at the cross pieces, you can't later decide to put your own wood on your side to make it look nicer to you.