What does Jesus mean that those that can be trusted on small matters can be trusted in large matter? Imagine Madoff coming to your living room and saying, "I got an investment that I want you to invest all your money in."

You test him. You left some changes on the table and pretend to do something else. You return and see the changes are still there.  Ah I can trust Madoff in small things. He must be trustworthy on big things. That would be stupid, right?

Many people don't steal small things not because they're infinitely trustworthy. People don't steal small things, so that they have their reputation intact and can steal big things.

Madoff didn't take the change not because he is trustworthy. Madoff didn't take the change because the change is small. He aims to steal big. So those who are trustworthy on small things are not necessarily trustworthy on big things.

I once lost $30k due to a fraudster that built trust by being honest on small deals. When the deals got big they ran away.  Likewise, most corrupt officials that steal billions won't steal chickens or bread.

On then face of it, this appears to contradict some of Jesus teaching on trust: 


  Luke 16:10
  "Whoever can be trusted with very little can also be trusted with
  much, and whoever is dishonest with very little will also be dishonest
  with much.


How is this apparent contradiction resolved?

Note: I honestly trusted this interpretation on Jesus words and lost almost $1 million of profit because my ex-employee become my competitor. Consider this a form of "customer complaint" on Christianity.
With parables you have to remember that they are directed at a specific audience, and make a specific point. Trying to extrapolate to draw conclusions outside the purpose of the parable would lead to a wrong conclusion. Parables are also used to illustrate general principles, not to lay down hard and fast rules.

In the Parable of the Talents, the point is about the behaviour of the servants. Jesus makes that pretty clear from context. The conclusions the hearer should draw are about parallels to the servants, not to the master. So (to simplify a little) the lesson from this parable is "work hard with what you are given to generate 'profit' for your master". You could also reasonably infer the lesson: "show yourself trustworthy in small things so that you will be trusted with larger things". (That's different from the lesson you are talking about.)

To derive a lesson that "anyone who is trustworthy with small things is also always trustworthy with large ones" would be outside the scope of the parable. It's focussing on the wrong part of the parable. The character in the story doesn't say it is a general rule, but only as something specific to another character: "Because you have shown yourself trustworthy in small things..." We shouldn't infer that it is applicable in all cases.