Under US copyright law, lack of a license is a significant problem. In general, you may not copy any literary work without the copyright holder's permission (computer programs are classified as literary works). The purpose of the EULA is to provide that permission. Suppose that the original stick owner illegally copied a program onto the stick (or hard drive), lost (sold) it, you found (bought) it, etc. and now you own the storage device. Turn to 17 USC 117 which allows a limited exception to the permission requirement:
it is not an infringement for the owner of a copy of a computer
program to make or authorize...
While you might be the owner of the stick (disk), you are not thereby the owner of a copy of the program that exists on it. To be the owner of the program itself, the owner of the program (the author) must transfer ownership of the program, that is, the copyright. The author could 'sell a copy of the program', but they usually (always, as far as I know) do not sell the program, they sell a license to use the software, and they do not sell the software itself. (A subtle distinction, and the law is full of them).
An illegal copy of a program does not become legal by being laundered through lost-and-found, or by being sold. If it was illegal in the first place, it is illegal until you get a license from the copyright holder. 17 USC 109 does allow the transfer of a legal copy:
the owner of a particular copy or phonorecord lawfully made under this
title, or any person authorized by such owner, is entitled, without
the authority of the copyright owner, to sell or otherwise dispose of
the possession of that copy or phonorecord.
This does not make it legal to transfer illegally-made copies, and this law pertains to the case where a person actually owns a copy of the software, rather than just having permission to use it. This clause does not say that a license is always transferable. Sometimes the license that a person buys will allow the license to be transferred, and sometimes it doesn't. To give a concrete example, certain software is sold via a significantly-cheaper educational license, and that license is not transferable (so students cannot get rich selling cheap copies of software to businesses).
Being in legal possession of a device which contains illegally-copied software is not against the law, what is against the law is making further copies. Typically, use implies further copying, since storage devices cannot perform the action that the program does. If you are interested in the copyings that take place when a computer program is executed, you could ask on one of the techie forum out there, but in general, a copy is transferred from the storage device to some buffer and various parts of the program are copied into memory as they are executed. This all happens behind the screen, just like installing a program: it all involves copying.
The courts could even decide (but they have not) that Congressional intent was to not include the automatic copying that comes with program execution. But §117 is already in place, and cannot reasonably be read to mean that "if you have an illegal copy of a program on a permanent storage device that you own, and your computer can run the program without copying to another storage device...".