This looks like old damage which has not been able to heal completely or even more likely, damage and stress from being planted too deeply. We notice that there is not natural flare or widening at the point where the trunk meets the ground.
As it stands now, the internal heartwood is rotting, which can make the tree structurally weak in storms. The wood that is wet and rotting will draw borers and carpenter ants who will eat it or use it, which is natural, but they are not the main problem and don't need to be controlled.
We do not have a recommendation on how to fix this and think you might consider removal if their fall would be a hazard to people or property.

You could also consider having a certified arborist, who is a tree health expert come out and do an on-site evaluation of all the factors. You can search for one at www.treesaregood.org

From the pictures it looks like you have Koelreuteria trees, also known as Goldenrain trees.  These are fast growing small - medium sized trees that are now widely planted thru our region,

The tree with the long open cavity toward the base has obviously been damaged in the past and is going thru the normal recovery process. There really is not anything that you can do for this tree at this point other than let it grow and continue with compartmentalization (wound recovery).

The other tree appears to be expressing slime flux. Please see:
http://extension.psu.edu/pests/plant-diseases/all-fact-sheets/wetwood-or-slime-flux
This particular condition can be brought on by stress - such as- wounds from mowers or weed eaters. At this point I would make sure that there is minimal possibility of mechanical damage by mulching around the base of your trees. See this link on mulching:  http://www.treesaregood.com/treecare/resources/propermulching.pdf 

Thanks for the advice and the tree identification. 

Nathan

Please feel free to call or email me directly also. My office is at the Carroll Co. Ag Center.

410 386 - 2776