I don't think that this is an IDLE error.  It 
can be more generally exhibited as follows:

Without the subprocess we get the expected:

IDLE 3.0a4      ==== No Subprocess ====
>>> eval('a')
Traceback (most recent call last):
  File "<pyshell#0>", line 1, in <module>
    eval('a')
  File "<string>", line 1, in <module>
NameError: name 'a' is not defined

With the subprocess there is an interpreter 
error when IDLE applies eval to 'a':

IDLE 3.0a4      
>>> eval('a')
Traceback (most recent call last):
  File "<pyshell#0>", line 1, in <module>
    eval('a')
SystemError: error return without exception set

I did a cutdown where I ran the eval in a 
subprocess and didn't reproduce the error.  I 
suspect it's thread related (the subprocess 
uses its main thread to execute user code, and 
another thread to manage the socket connection 
to the GUI process).

issue1733757 is suggestive.

This is a 3.0 issue, it doesn't occur in the 
trunk.