The main answer is found a little later in the chapter:
27 The Lord said to Aaron: Go into the wilderness to meet Moses. So he
went; when meeting him at the mountain of God, he kissed him.
So Aaron, a prophet in his own right, received a revelation from God to go out and meet Moses in the wilderness. The OP asks if he escaped. Technically perhaps, but Hebrew slaves in Egypt were not as been as tightly controlled American slaves were in the 19th c. Also, being an old man (about 83 years old) at the time, Aaron would not have been required to do daily labor and could more easily travel than an able-bodied younger man could. He may even have received permission to make a pilgrimage to the Mountain of God.
Another thing to consider is that there was a new Pharaoh by this time, a king who no longer sought to kill Moses:
19 Then the Lord said to Moses in Midian: Return to Egypt, for all
those who sought your life are dead.
The new pharaoh might have been more favorably disposed to Moses' family and the Hebrews generally. It is interesting in this context, that the pharaoh does not harden his own heart toward Moses, but God himself hardens the king's heart.
21 On your return to Egypt, see that you perform before Pharaoh all
the wonders I have put in your power. But I will harden his heart
and he will not let the people go.
Conclusion: Aaron met Moses in the wilderness because God instructed him to do so. He was able to leave because, being an old man, he would not have been carefully supervised or necessarily missed at work. Aaron's status as a slave would not be affected by any of this.