For people learning Russian, there is an important exception to the general idea about not using ы after velars and hushes. For grammatical endings, ы after ц is normal. улицы отцы зайцы.except you can never write ы after a letter к, or any other gutturals (Г, К, Х) or sibilants (Ж, Ч, Ш, Щ, Ц) for that matter (called the 7-letter spelling rule).
Otherwise, it is very rare to see ы after velars and hushes. In the list of 50,000 words, only a few appear. I don't know what they all mean, but here is the list. I don't know why they are on the list, I'm just reporting what I found. Some look like they are grammatical plurals квасцы ножницы сенцы уздцы святцы, and so these would normal.
There were no examples of чы шы щы жы.
куцый круглолицый краснолицый бледнолицый белолицый
цыплячий
цыпленок
цыганов
квасцы
святцы
цыган
ножницы
цыбашев
стануцын
цыбулский
цы
люберцы
Голуцын
царицын
сенцы
лисенцын
цыц
уздцы
цыкнуть
кыся
кыргыстан
кыш
викыч
кыпс
хы
гы