Is there any record of children of this age completing the journey alone, as opposed to starting it out with a guardian who dies along the way ( which seems more plausible)? If so, is there any record of children such as Vito completing the journey alone with no one there to receive them at the other end?
Is there any record of children of this age completing the journey alone
Yes. Vito Corleone arrived in the US in 1902, and at that time unaccompanied minors were frequent enough that the immigration law of 1907 was rewritten to specifically stop children under 16 from normal entry. There is a statue on Ellis Island of 17-year-old Annie Moore, who arrived unaccompanied by adults but accompanied by her 12-year-old brother in 1892 - but maybe you are looking for younger kids. Chaim Kasinitz supposedly arrived alone in 1907, aged 9.
is there any record of children such as Vito completing the journey alone with no one there to receive them at the other end?
Children with no guardians to receive them were held in detention and could then be taken up by local charities, missionaries, synagogues etc after a hearing.
For more on this, there's a book called "The Children of Ellis Island" by Barry Moreno.
Edit: To give you another idea about the scale of unaccompanied child immigration, a 1904 Washington Post article describes 200 immigrant children who were at that particular time being held in detention on Ellis Island, supervised by 12 "matrons". Second edit: got tricked about Annie Moore's age.