Barb I don't mean this to sound insensitive -- but how does she "know" about Buddy? You took him to the vet but he didn't come home. Did you bring him "home" or just tell her?
The "short" answer is that typically their grief is first confusion if they didn't get to 'see' the deceased, particularly if it wasn't something like cancer or an illness they could smell. The grief typically is different with each one -- often behavioral changes, depression -- can be like it is in us or it can be totally missing. However -- if she was *worried* about him -- he was gone all day, that could have tied her up in knots and caused digestive issues over the course of the day.
They're often smarter than we give them credit for -- and they **DO** hear us talking and draw conclusions, so it's likely she knew *you* were completely wound up, and had talked about losing him (you lost a cat not long ago that you had to help over the Bridge if I recall??) So she's likely smart enough to know he might *not* come home so she could have been pretty upset.
With a lot of hindsight -- AND with the understanding that I expect a lot of understanding --language-wise -- from my dogs, I always make sure they get to see the dog who has passed **just** so they get closure and know she/he's not in pain somewhere. They may know us and love us, but I don't expect my dogs to "trust" me like that - I want them to see.
Usually there isn't much reaction when they see a deceased. It's almost like they sniff and walk away like "Well, THAT isn't where *he* is any more!! He's not IN there any more" (and more emphasis on the words just for clarity -- I think they are way more matter of fact about death than we are).
I had to help Foxy over the Bridge, but he and Billy were SO bonded I took Billy up with me when I took Foxy. The girls held him out in the reception area for me while Dr. Bailey and I said goodbye and Dr. B administered the pink stuff. But then I had them bring Billy back in the room so HE could see.
We took Kee Shu to the emergency vet (cos David wanted to be with me) but we brought her home afterward and I took her up to Dr. B to be cremated the next morning -- a lot of running around, but Luna, Billy and **particularly Tink** were bonded to her and it was the first of death Tink had seen.
When we lost Billy in March it was SO fast -- David and I were out (it was our anniversary) and we went home to GET Tink & Luna to go up to the vet at 10:00 at night to see Billy for the last time. They KNEW he'd gone up to stay with Sharika but this was a complete surprise.
Ok -- all that to say this -- they ALL grieve, and can grieve DEEPLY. There tends to be "no fun" in the spirit for days. It can change behavior for weeks and months -- often they will go lie "by" or "on" the favorite place of the one who is gone. Sometimes pack restructuring. Sometimes **nothing**.
Tinker probably grieves the hardest of any dog I've ever had. It really whacks her for a loop for weeks where she is very subdued, sighs a lot, etc. She and Billy weren't all that close -- but she **Missed** him greatly.
To answer your question bluntly -- yes, they can become physically ill with grief, but typically I'd associate it with something a *bit* longer term. I'd watch Heidi very closely -- "stress" can bring on a ton of things (we see dogs over on the IMHA page pretty frequently where the owner can trace stress as the precursor to the IMHA onset -- via behavior, etc., and my holistic vet has told me many stories of emotional trauma resulting in auto-immune stuff).
One more thing to think about -- Heidi has shown *no* reaction at all to the Frontline? She's the only one off her food? Not grabbing at straws -- just trying to help you look at all angles.
But honestly, given the fact that she's playful -- I'd give your vet a call and at least *tell* him how fast and hard she's gone off her food. Taking her in for a fecal might be smart. Pure stress can cause a huge increase in gut bacteria but that might manifest a bit different. It would just be a darned good idea to have the vet in the loop.