use of apostrophe

Not quite. How it should read depends on what you want to say.
"He ran away with others' belongings." means he stole from other people.
"He ran away with the other's belonging

But what I meant to ask was, is it okay to say this way or should it be "He ran away with belonging of others."?

You could say either "He ran away with others' belongings." or "He ran away with the belongings of others."
Changing it to "He ran away with other people's belongings." might be better.
Two things:
1) Note where the apostrophe goes when the noun is plural and

Like we never say, Chair's leg has broken. We always say, leg of the chair is broken.

so I thought may be it's always "belongings of others and not "others' belongings".

We could say "the chair's leg has broken" although "the chair-leg has broken" or "the leg of the chair has broken" would be more usual.

the usual will be the chairs leg is broken

yusra sayed the usual will be the chairs leg is broken

No, that would need to be "The chair's leg is broken".

so, is it grammatically perfect to say, "chair's leg is broken."?

The chair's leg is broken. (or my, her, your, etc. chair's leg is broken)

yusra sayedthe usual will be the chairs leg is broken

Not exactly. I would say The chair leg is broken. (Not chairs, but chair's is possible.)

CJ