Paradoxical participle [duplicate]

From Lexido:

meet: Come into the presence or company of (someone) by chance or arrangement.

Given that, you need to make it clear what walking down the street modifies.

If you're the one walking down the street, you could say, "Walking down the street, I met a friend." There is no implication that your friend was also walking down the street. You friend could have been sitting on a wall.

If your friend was walking down the street, you could say, "I met a friend who was walking down the street. Again, there is no implication that you were also walking down the street. You could have been sitting on a wall.

If you want to make it clear that you and your friend met while you were both walking down the street , you could say something like, "Walking down the street, I met a friend (who was) also walking down the street."