It's not a well-known one, but we have.
- 親【おや】苦【く】、子【こ】楽【らく】、孫【まご】乞食【こじき】 "Parents toil, children ease, grandchildren beg."
Also with many variations:
- 祖父【じじ】は辛労【しんろう】、子は楽、孫は乞食
- 「親苦労、子楽、孫ほいと」「親苦労、子楽、孫潰」「親苦労、子楽、孫貧乏」 etc.
- 親草鞋【わらじ】、倅【せがれ】草履【ぞうり】で、孫雪駄【せった】、曾孫【ひまご】の代には裸足【はだし】なりけり
"parents (wear) sandals, kids shoes, grandchildren boots, great-grandchildren would become bare feet"
But more famous sayings with similar moral are: