Shinies available beyond events?

Yes. A friend caught a shiny Bulbasaur the other day.

Once a shinny's introduced, its never removed from the game. its just less common to find. Got a shiny pinco and murkrow yesterday

If you need more anecdotal evidence, I have caught shiny Magikarp, Charmander, Wailmer, Sableye, and Shuppet all well after their introductory events.

The last non-community day event I caught a shiny...September 6th, a bulbasaur. Did get several shiny wingulls, but most other extended events I whiff. None this Halloween, nor last Halloween. Got a non-event Makuhita August 10th and an Aron July 24th. Then for the mini-event got two Plusle and one Roselia. Not very many, I click on most shiny eligible species I see...especially Murkrows, zip though.

I caught a shiny shuppet a few days before the Halloween event started this year.

yes i caugt a shiny eevee after the event (already had 20 :( ) and a shiny charmander i missed the charmander event so i was very happy wiht that

If you need more anecdotal evidence, I've caught the following event-related shinies outside of their events:
1 Minun
1 Eevee
2 Bulbasaur (1 from research)
3 Aron (2 before the event)
5 Magikarp
2 Roselia
3 Wailmer

Shinies are simply rare in the wild, the more pokemon you catch, the more chances you have of seeing a shiny.