The angel of the LORD found Hagar near a spring in the desert; it was the spring that is beside the road to Shur. And he said, “Hagar, servant of Sarai, where have you come from, and where are you going?”
“I’m running away from my mistress Sarai,” she answered.
 Then the angel of the LORD told her, “Go back to your mistress and submit to her.” The angel added, “I will so increase your descendants that they will be too numerous to count.”
 The angel of the LORD also said to her:
“You are now with child
and you will have a son.
You shall name him Ishmael,
   for the LORD has heard of your misery.
He will be a wild donkey of a man;
his hand will be against everyone
and everyone’s hand against him,
and he will live in hostility
toward all his brothers.”
 She gave this name to the LORD who spoke to her: “You are the God who sees me,” for she said, “I have now seen the One who sees me.” That is why the well was called Beer Lahai Roi; it is still there, between Kadesh and Bered.
 So Hagar bore Abram a son, and Abram gave the name Ishmael to the son she had borne. Abram was eighty-six years old when Hagar bore him Ishmael.  Genesis 16:7-16

"If you had a chance to go back in time and shoot Hitler's mom, would you do it?"  Tough question.  Is it fair for an innocent woman to die?  What about the innocents who will die as a result of her child?

The same question occurs here when it seemed God could let her and the child inside her, Ishmael, die alone in the desert--a child who will spawn the legacy of Arabs, whose descendants will torment Israel and will birth a faith called Islam.  (God had another chance to allow them to die in Genesis 21, after the birth of Isaac, and Hagar and Ishmael are near death in the desert.  Again, God saved them).

It wouldn't be fair or just for God to kill Hagar and Ishmael.

• They did nothing wrong.  Why should they die for what their descendants will do?  What about my descendants?  Would it be fair for me to die for their crimes?
• Their situation was caused by Sarai.  Shouldn't she die?
• God showed his mercy to Hagar and Ishmael and protected them, just as he always promises to protect widows and orphans.
• God gave Hagar and Ishmael no reason to rebel against Him.  Their descendants knew of God's mercy yet chose to follow revenge and  rebellion instead.

God allows man to have his freewill, giving him the right to choose.  He doesn't punish them before they choose.  And, he is a just God who does not punish you for crimes you did not commit.  For those reasons, in addition to his love and mercy, God rescued Hagar and Ishmael.