TIDA-01168: TMS320F28027, During debugging, encountering a connection error.

I would suggest to use the “test connection” feature within code composer studio (CCS) just to verify the emulator can actually detect the MCU in the scan chain. In this case, it may mean that the MCU is simply in a bad state. Please also check the basics: clock, power, and reset.

You can use the link below for debugging tips:

https://software-dl.ti.com/ccs/esd/documents/ccsv7_debugging_jtag_connectivity_issues.html#troubleshooting-the-connect-phase

Assuming the target configuration is correct-

Please check that if you are using the instaspin ROM? There might be an issues with that blocking connections to an emulator.

As a quick fix, most of the time resetting the device will help to make the successful connection. 

Better yet you can also try to put the device in “wait-boot” mode or “boot from SCI” then try to connect.