Yes, a clot in time can be systematically dissolved, may not move or seriously block, and if necessary medical dissolving agents.
"The process of dissolving blood clots that already exist is called thrombolysis. Three groups of thrombolytic agents are available, including enzymes, which act directly upon the fibrin strands within the clot, plasma activator agents, which increase plasma activator activity, and plasminogen activators, such as streptokinase, urokinase, and tissue plasminogen. All these drugs digest clots by increasing the amount of plasmin (plasmin dissolves clots) in the blood. To produce plasmin, the substance plasminogen must first be activated. Plasminogen is converted into plasmin by certain enzymes known as plasminogen activators".