Big stalks in hay- can piggies eat them?

[Eddie & Elvis]

Occasionally I find big stalks like the one in the picture I've attached. I take then out when I find them but recently I didn't spot one until I saw the piggies eating it. They seemed really excited about it so I want to know if they're safe for them to eat.
Thanks in advance

 

[Piggies&buns]

It depends what it is a stalk of. I normally pull them out if I find them

 

[Eddie & Elvis]

It looks like a really thick bit of hay rather than a twig from a tree. I always take out twigs since I don't know what kind of wood it is

 

[Piggies&buns]

It could be something thicker stemmed like cow parsley, for example, but probably safer to remove it from the hay just in case

 

[Eddie & Elvis]

I guess it's safer since I don't really know what it's is. Thanks