I answered to a similar question
here, so that may help you.
However, none of the following three have female leads that are forced to stay with the male leads because they're poor. It's more because the male lead is in love/attracted and makes her stay with him against her will, often by threatening her relatives/friends because he's powerful and wealthy.
- Lady & Liar has rich guy/poor girl theme AND forced marriage (well technically, engagement) BUT memory loss! It's not so bad because the story actually centers around that, so it's not random last minute amnesia
- Sealed With a Kiss has rich guy/poor girl theme, and the male lead forces the female lead to stay with him, but without marrying her
- Cruel Romance has rich guy/poor girl theme, and he falls in love very soon and is very forceful, but he doesn't force her to marry him