Can I stay in the UAE to attend my labour case after my visa was cancelled?

You can apply to stay. Workers with a labour case still before MOHRE or the courts can obtain a temporary permit from the immigration authorities so a visa cancellation does not force them out mid-claim. The usual route is to get a letter from the court or MOHRE confirming the dispute is pending, then apply through the immigration authority (GDRFA in Dubai, ICP elsewhere) before your post-cancellation grace period runs out; the permit is issued for a limited, renewable period tied to the case. And no, leaving does not kill the case. You can sign a power of attorney for a lawyer or trusted representative to continue it; if you are already abroad, the power of attorney is signed there and legalised through the UAE embassy. Judgments can be issued and enforced in your absence, and any award transferred to you. Practical steps: secure the pending-case letter now, apply for the permit promptly, and keep copies of your contract, payslips and the cancellation paper. A labour lawyer licensed in the UAE can handle the permit application and run the case whether you stay or go.