So, I just gave my players an Elder Thing MacGuffin. What does it do?

[Quentin Coldwater]

So, I'm running Strange Aeons. My players recently found two Elder Things and let them escape (they didn't make sense to be overtly hostile). One of my party tried to befriend one, and for the fun of it, the Elder Thing gave that person a fist-sized chunk of flesh before it flew away. I described it as a pulsating piece of flesh, with a latticed structure around it, like this mushroom. Problem is, I haven't really decided what it does. >_> So, I'm here to ask you: what's a fun thing/ability to give to my players? I don't mind homebrewing or increasing their power level a bit. It's mostly a fun thing and a reward for doing fun stuff.

My players think it's an egg of some kind, and they want to hatch it. I was thinking of maybe giving them a summon ability they could use an X amount of times a day, like a Summoner gets. They've also befriended an extraplanar Voonith, so this might summon that as well. But I'm open to all kinds of suggestions. Bonus feats, spell-likes, anything is possible. I've described these things as intensely weird and unknowable, so anything's on the table. Hell, I'd even consider it becoming an animal companion of some kind.

[Joey Cote]

Merges with a character during their sleep and gives them -

1) A vestigal arm with some strange ability
2) A third eye which gives some bonuses but also "visions"
3) An altered tongue which gives some bonus or even ability but also causes the character to speak certain truths that might cause problems
4) A pulsing mass attached to the character's chest that they find they can remove and shape and effectively acts as a tumor familiar ... but with extra knowledge.

[LBHills]

Well, Elder Things (unlike the vast majority of Lovecraft's creations) aren't actually malevolent. So this probably wasn't the moral equivalent of passing a hand grenade to a monkey.

Maybe it's the equivalent of an Elder Thing 'tricorder' - when it detects a creature that it 'remembers' it sends a stream of telepathic information, essentially a free knowledge check about the entity. If you want to beef it up a little more, it might provide translations of writing that it recognizes (usually only those of creatures from space, or certain extraplanar languages), or have useful information on counteracting poisons, infestations, etc. from aberrations.

[Mudfoot]

If left alone, it moves slowly around on the floor tracing out eldritch patterns of slime. These mean something, but it's in an alien language, deeply cryptic and not immediately relevant.

After a while, it splits in two like an amoeba. The two parts gibber quietly to each other, still tracing out their sigils. The two become three, five, eight, etc.

If any are harmed, the survivors react immediately and stare accusingly at the perpetrator, who will have unpleasant (and potentially harmful) dreams and hallucinations for some time thereafter.

When sufficient spawn have appeared, the writing changes into a Gate spell, which triggers immediately.

[Mark Hoover 330]

It's been ages since I went through my Lovecraft phase but from what PF and the Lovecraft Wiki say this is a race of mostly non-aggressive colonizers. I doubt they'd have given away a weapon or some power armor or something.

The wiki does say they're gifted in genetics and biology. Could be they were leaving behind some portion of an experiment? If that's the case it could be like your players' "egg" theory. Perhaps it's a tumor familiar that has the Mascot archetype.

At first it bonds with the PC that earned it as a reward. I don't know what kind of a PC that is, but you could mirror the familiar's development after that class and any associated archetypes that get a familiar. For example, if the PC is a fighter the familiar gains the ability to use that PC's Combat Feats.

As the familiar hit's level 3 of development it bonds with the entire party. They can target it with spells and so forth. This is a solid reward for the whole group.

However this bond works both ways and the genetics that went into their little buddy are part Elder Thing or perhaps some other alien creature. After perhaps 2 levels of the familiar being a team familiar the PCs begin to experience dreams, rapidly becoming nightmares, of other worlds and maddening thoughts.

This might lead to checks to see if they're Fatigued or developing some kind of insanity. It might ALSO lead however to further reward. Perhaps if the PCs look into this phenomena and figure out what's going on they can somehow master it, control it, and use this alien communication as a form of divination or psychic ability long term.

[Kitty Catoblepas]

Players should find that they're able to milk the thing. It gives off a sweet, delicious substance (similar to horchata) that provides some benefits (consuming a dose counts as a Goodberry, gives an alchemical bonus to something-or-another, provide a bonus to Perform and other creative skills, etc.). The point is that the players should want to protect it because they think it's a wonderful thing to have around (without being too over-the-top wonderful, thus appearing to be an obvious trap). It does this as a natural response to protect itself from predation. Hopefully, this would also make them want to adopt and protect any more of these things that they find in the wild.

For nurishment, it should consume negative emotions. When a creature around it succumbs to a negative emotional effect (fear effects, despair effects, etc), it should "consume" it by casting a limited/targeted form of Calm Emotions (it should remove penalties, although it shouldn't negate combat). Players should note that if they have enough of these around, they have a difficult time feeling sad or angry. Alternately, you could have it consume parts of dead monsters, disolving them like acid (although this may cause players to get squeamish about how it makes its "milk").

It has no "endgame." It's just trying to grow, eat, and survive. It's not malicious. It has no ulterior motive, though it may seem a little scary at times.

Kunstformen der Natur has some interesting shapes, if you're looking for pictures to show your players. It's available on the WikiMedia site and is in the public domain.