wear out vs. be worn out

[jokaec1]

For example,

1) My shoes wore out. My shoes have been worn out.

Are they both correct? If so, what is the difference and which one is more common?

2) My patience began to wear out. My patience began to be worn out.

Are they both correct? If so, what is the difference and which one is more common?

[teechar]

My shoes wore out.

My shoes wore out after almost three years of daily use.

My shoes have been worn out.

Unnatural.
Consider saying: "My shoes are worn out."

My patience began to wear out.

My patience began to wear out after they continued to ignore my complaints.

My patience began to be worn out.

Unnatural.

[tedmc]

I think "have been worn out" and "to be worn out" are not only unnatural but are wrong.
Wearing out is a natural process. Both phrases imply something or somebody caused the wearing out, which does not make sense.

[Rover_KE]

That is incorrect, Ted.

"Have been worn out" and "to be worn out" are just fine in the right context.

[tedmc]

That is incorrect, Ted.

"Have been worn out" and "to be worn out" are just fine in the right context.

The contexts have been given by OP.
Could you give examples of context where the phrases can be used?

[Matthew Wai]

'My shoes have been worn out for a long time, but I am still unwilling to throw them away.'
'My patience is going to be worn out by your annoying questions.'

Not a teacher.

[emsr2d2]

In BrE, we generally say "My patience is/was wearing thin".

[mawes12]

Isn't that the same as "waste" or "use"?

[Matthew Wai]

I think "have been worn out" and "to be worn out" are not only unnatural but are wrong.
Wearing out is a natural process. Both phrases imply something or somebody caused the wearing out, which does not make sense.

I think 'worn out' could be used as an adjective and 'wearing out' could have a cause, so both phrases could be right, but I am not a teacher.

[Rover_KE]

Isn't that the same as "waste" or "use"?

No.