Can some blood thinner dissolve the blood vessels as well?

The term "blood thinner" is actually completely inaccurate, but was started to try & explain to the lay public a drug. In actuality, "thinners" actually stop clot formation at some point in the process. For aspirin, it inhibits the platelets from acting in the clot (stops them from becoming sticky). So there really is no dissolving or thinning of anything. The body makes the clot go away via a natural process of clot retraction.