Air Traffic Controller reported missed communication between controllers resulted with an aircraft entering the runway safety area while another aircraft was landing on the same runway. The crossing aircraft held short of the runway but beyond the hold short lines.

Narrative

I was working Ground control giving taxi instruction to Aircraft X who vacated runway 19 taxiway Juliet; I instructed him to taxi via Lima hold short Runway 24; and he read back correctly his hold short instruction. I coordinate with my local controller behind the departure cross runway 24 at Lima; and he said to the best of my knowledge and hearing 'behind the departure cross runway 24' and the controller appropriately positioned the Stripholder 'offset' to indicate a crossing is taking place (memory aid) to indicate he gave a crossing. After I witnessed the departure aircraft pass taxiway Lima I issued the crossing to Aircraft X. Well; there was traffic landing short final that I did not see and was not told about. As I looked up at the radar I saw a target with a * and 001; and I am questioning myself in my mind; 'why is that departure target at the wrong side of the runway?' As I round out my scan I see Aircraft Y coming down to land; and I hastily extended my arm and the controller saw me; gesturing; and I am trying to spit out 'Aircraft X hold position!' The pilot responded; by saying 'we saw him' and the aircraft stopped short of the Runway 24 white side stripes but in the RSA (runway safety area).I believe local did not hear me say Behind departure. but rather just 'behind'.Recommendation - I should have had done a more thorough scan. This is a FIRST for me.