If you are concerned about the structural stability of the trees, we would recommend having a tree health expert, a.k.a., a certified arborist, come on-site to evaluate them. Most larger tree companies have certified arborists on staff and you can search for one at the credentialing organization at http://www.treesaregood.org   
Your first photo shows a small slice of internal wood that looks compromised but it's impossible to tell how much.
Your second photo shows a wet area, which could be this: 
https://extension.umd.edu/resource/tree-trunks-wet-wood-or-slime-flux/  This is not always of great concern unless the tree is otherwise unhealthy.
How does the leafy canopy look on these trees? Is it full of normal size/color leaves without a lot of dead limbs?
This page can help people to know when a tree may be dying and should be removed:
https://extension.umd.edu/resource/how-do-you-decide-when-remove-tree/


Christine