Yes, they do. I have struggled with it.
This is a very, very hard question to answer candidly and honestly at SI. It's almost an axiomatic lose-lose. Any account you give, of why you felt these positive feelings toward the OP and why some of them linger after the affair, goes against the kind of neural reprogramming SI offers, excels in, and insists on. It also has the potential to be very hurtful to BSs, which is the last thing I for one want to be.
But it seems like your question deserves some kind of answer, so I will offer at least an outline of one.
I had a mid-life emotional affair with my childhood first love. It was long distance, conducted mostly through text messages. If was not overtly sexual, in the specific sense that it did not include sexting or pics. And there was no physical contact at all.
The life-blood of this affair was therefore exchanging emotional intimacy at a time when my and APs marriages were both under stress, and we each felt isolated and alone. It was an extreme test case that highlights the general emotional components of affairs, separated from the physical/sexual components.
Here in no particular order are some of the qualities my affair had which made me feel something like grief at the loss of the relationship:
1. It was a very limerant connection. Limerance unleashes tornados of brain chemicals which are very, very addictive, and I have an addictive personality/brain wiring. Recovering from limerance feels like grief, even when you know rationally that what you are grieving is an image you invented in your own head and projected onto the AP.
2. In my case there was also a legitimate preexisting pre-affair relationship at various times in life between me and AP, of decades total duration. This meant that I had and still have an impression of her qualities, good and bad, from contexts predating the emotional affair. Its not the case that AP and I lied at all times, or from the beginning, over the total scope of the relationship.
3. During the affair, each affair partner was able to show the other, for a time, certain emotional capacities -- interest, care, playfulness, intense caring, vulnerability -- that were impaired in the primary relationships. Those capacities were actually real. However they were bought at the cost of making each other unhealthy and morally wrong, because, we were each turning the other further away from connection with our spouses, when a true friend would have supported turning back toward the marriage and the spouse.
4. AP and I each let need and selfishness overcome real friendship. Real friendship was destroyed and will remain impossible now and forever. But she was, once and for a long time, a real friend. The loss of that remains a source of grief.
I will only say in summary that I am very unsatisfied with this answer I have given you. I do not offer it as any kind of justification. You asked a question that is almost impossible to answer without insulting the framework SI teaches us to recover from affairs. I assure you, I do see my own bullshit and sit in its stink and corruption.
But I felt someone should answer, and, my type of affair might show you how this can be. It's wrong. All affairs are wrong and unhealthy. But I did experience grief along with the consciousness of wrong and those are some circumstances -- not justifications -- but some circumstances contributing to why the grief was there.