I'm hijacking this straight out of Wikipedia:

"There is no recognition of a legal term abandonware in copyright law. There is a long held concept of abandonment in trademark law, but it is a direct result of the infinite term of trademark protection. Currently, a copyright can be released into the public domain if the owner clearly does so in writing; however this formal process is not considered abandoning, but rather releasing. Those who do not own a copyright cannot merely claim the copyright abandoned and start using it without permission of the copyright holder, who would then have a legal remedy. Hence abandonware is sometimes considered to be synonymous with "old warez".
Hosting and distributing copyrighted software without permission is illegal. Copyright holders, sometimes through the Entertainment Software Association, send cease and desist letters, and some sites have shut down or removed software as a result. However, according to Wired magazine, most of the association's efforts are spent on new games, due to those titles having the highest value.
Companies do sometimes voluntarily relinquish copyright on software, putting it into the public domain, or re-license it as free software or freeware. id Software is an early proponent of a similar practice, releasing the source code for the game engine (but not the actual game content, such as levels or textures) of some older titles under a free software license. Other examples include Amstrad, who support emulation and free distribution of ZX Spectrum hardware ROMs and software, and Revolution Software, which released their game Beneath a Steel Sky as freeware and gave the engine's source code to the authors of ScummVM to add support for the game. Transfer of public domain or free software is perfectly legal, distinguishing it from copyrighted abandonware. See list of commercial games released as freeware.
There are active groups that try to lobby companies to release their software as legal abandonware. These efforts have met with mixed results. One example is the huge library of educational titles released by MECC. MECC was sold to Brøderbund, who was sold to The Learning Company (TLC); when TLC was contacted about releasing classic MECC titles as freeware, it was determined that the documentation proving that TLC owned the rights to these titles could not be located, and therefore the rights for these titles are "in limbo" and may never be able to be legally released."
Full artical: Abandonware - Wikipedia, the free encyclopedia

In short, the answer is that you may not distribute any software unless the compainy has given permission or the copyright expired. Since neither of these has happened to any PS1 game, none of them are to be freely distributed.

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