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If you could get the correct visa you could work either full time or part time depending.
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"Depend" can come at the end of the sentence like in this example :
Are you coming over for dinner ?,I don't know,it depends.

Also,you can finish the sentence by saying "it depends on....something or else.
BUT ,I don't think it's possible to end a sentence by "depending".you should rather put it in the middle adding "on".
Prices vary depending on the area you choose.
How would you finish it?

If you could get the correct visa you could work either full time or part time depending.

Is this nice?

Depending on the type of visa you get, you can either work full or part time.
Whether you can work full or part tme depends on the type of visa you get.
how do you finish it
If you could get the correct visa you could work either full time or part time depending.

what about

Depending on the type of visa you get, you either can work full or part time.
Whether you can work full or part time depends on the type of visa you get.
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