A different parse can be used in a different version of this function (or it could be turned into a higher order function).

For example, the collect body could be this if the input is only integers:

:collect (parse-integer string :start start :end (or end (length string)))

The higher order function version could use this as its collect:

:collect (funcall function string :start start :end (or end (length string)))

That would only require changing the function signature to:

(defun parse-and-split-string (string function &optional debug)

Then it could be called like this:

(parse-and-split-string "123 23487 39"
                        (lambda (string &key start end)
                          (read-from-string string t nil :start start :end end)))

Finally, using the higher order function version, we have just reinvented a subset of yet another split-sequence if we have a "plain" parse function. That function is subseq:

(parse-and-split-string "123 456 789"
                        (lambda (seq &key start end)
                          (subseq seq start end)))
;; => ("123" "456" "789")