Doing that does not mean the stems won't flop over again next year, just means you won't get any flowers. They tend to do this in drier spots, because really, they like damp soil that doesn't completely dry out. Best to just cut it all down as soon as the flowers fade, or immediately if you can't stand the way it looks.

Jude, I have this and I agree re. Staking, so what i tend to do is just encircle the plant with twine and that keeps it more upright without the ‘trussed up’ look that staking gives. Alternatively, you could buy a semi-circular metal support which will do the same job...from GC or Amazon. I’m not sure that the ‘Chelsea chop’ in spring would work on Lysimachia because it only flowers once so as Bamboo says, you would probably just lose the flowers. But I’ve never tried it. I did do it on some geraniums this year, but they flower all summer.