The Chafetz Chaim says in his sefer Zechor L’Miriam chapter 20 that another proof to the power of Bitachon is from the story of Lot and the two angels that came to him. When the people of Sedom surrounded his house and wanted to kill these angels (who were actually perceived as guests) Lot went out and said, “Don't do anything to them. They came into the shade of my beam/my roof,”
which means they relied on me. I'm going to take care of them. They're my guests, so please protect them. Lot wasn't the best of people, as it says, Lot traveled Mikedem/from the east and Rashi says, Kedem means from the original One of the world, which is God). And yet he felt that the fact that they were relying on him was a reason for him to come through. The Torah tells us this, obviously, to teach us this lesson, that surely if we rely on Hashem, Who is the Source of all mercy and compassion, He's going to come through for us.
Rav Bloch quotes from Rabbi Chaim Brim, who heard from the Brisker Rav that Bitachon works based on the principle of Arevut, which means co-signer.
Legally, if I'm bound by something, I need to have some mechanics of acquisition to make me owe the money. I can't just go to you and say, I owe you a hundred dollars. That doesn't work. I have to make what's called a kinyan.
You have to do something. At a wedding, the hattan obligates himself by making a kinyan. You can't just say, I owe money. It doesn't work that way. If you borrow money, you owe it, but you can't just obligate yourself. So how does it work when I borrow money from somebody, and there’s a co-signer? If the borrower doesn't come through, the co-signer has to pay, but the co-signer didn't make a kinyan, he just signed as a co-signer. So how does it work?
The Gemara in Bava Batra 173B says that the pleasure that the co-signer gets that he is being believed (because people say, ‘This man is a co-signer, I guess he’s trustworthy man) is what commits him, and he makes a kinyan with that. How does that work?
So let's just give a little bit of background. Anytime I buy something, why do I need a kinyan?
The answer is that you have to show that there is a commitment. There has to be a conviction to what you're doing. You're not just saying words. You need to make a kinyan, which shows what's called Gemirat Da’at. It’s a way of showing conviction. Sometimes there are other ways of showing conviction. For example, the Gemara says, it can be something that's accepted in a country, like a handshake. On 47th Street, they use a handshake and say ,”Mazal,” and that signals that the deal is closed, even though it’s not a legal contract. Since it’s considered a way of showing conviction and a commitment to the sale, that is binding.
So the fact that somebody trusts a person and relies on him, makes it a binding acquisition of sorts. Therefore, if the borrower does not come through, the co-signer has to pay. And that's how Bitachon works. We are, so to say, giving God a certain pleasure by relying on Him, and that reliance on Him causes Hashem to be obligated to come through, just like the co-signer is obligated to come through.
Another example of this concept in the Torah is found in Rabbenu Bachye’s commentary on Shemot (chapter 1, pasuk 10), which explains why Paroah didn't just kill the people outright. Why did he come up with all his tricks with mothers and midwives and so on?
And he says, because here was a nation that came to live in his country, and they relied on him. They trusted him, so it would be considered a disgrace amongst the other nations to kill them publicly. He didn’t want to be embarrassed. That's why he had to come up with these secret tactics in how to do it.
So we see from here, says Rav Bloch, that this was even true for the worst of the worst, Paroah the Rasha. For him not to come through to people that were relying on him would be considered an Avla/iniquity, and he was embarrassed of it, so he came up with those different tactics.
Have a wonderful day.