It depends. If I was the jaded friend who lost trust in someone's character, they would have to prove to me that they are 100% behind what they say in advance. If the guilty party truly do feel gulit, they should want to go the extra mile to show their sorrow for their neglect, and their gratitude for willing to give you another chance. Don't let self-pride destroy a good friendship.
Now naturally (assuming that you are the highly intelligent individual I know you are, lol) make contributions that are within reason, in other words, don't let this person make a complete fool outta' ya'!