Reliable method to get the command for last pressed key?

Question

I'm writing some code where I have to identify the command for the last key pressed. Sometimes I need to look up a combination of this key with another one. I use the key-binding function for that. It works most of the time but not for all keys. For example it does not work for the backspace key:

(progn
  (read-key)
  (key-binding (vector last-input-event))) ;; > nil for backspace

I can work around this by checking for backspace manually but I wonder if there is a more reliable way that works for all/most situations?

I use last-input-event because it is after exiting a keymap through the default binding [t].

Edit:

Based on the accepted answer I'm using something like the following which seems to work very well:

(progn
  (read-key)
  (key-binding (kbd (edmacro-format-keys (vector last-input-event)))))

Answer 1

You can repurpose part of the kbd-macro infrastructure for this, specifically edmacro-format-keys. It already handles a lot of edge cases for you. For example:

(edmacro-format-keys (kbd "DEL") t) 
=> "DEL         ;; backward-delete-char-untabify"

and

(edmacro-format-keys (kbd "C-x C-s") t)
=> "C-x C-s         ;; save-buffer"

Answer 2

backspace and a lot of other keys are function keys for which, the event is a symbol so there is nothing in the keymaps for it.

(progn
  (read-key)
  (cond
    ((symbolp last-input-event) last-input-event)
    (t (key-binding (vector last-input-event)))))

The above still doesn't get you the function for the symbol of the function key.

(let (( key (read-key-sequence "hit a key:")) 
     (message "key %s was fun %s " key ( key-binding key t)))

But that uses read-key-sequence and it seems like you want to use last-input-event. Maybe take a look at the definition of describe-key in help.el