Outright desertion may not have been the best survival strategy, which probably is why so relatively few soldiers choose that option.

There would be several challenges for single straggler behind the frontline. First, the roads and area behind the battlezone was controlled and patrolled by Feldgendarme or "Feldjäger-Kommandos", or "Military Police". These were often under Waffen-SS control and basically had a free hand to kill anybody suspected of "Fahnenflucht"/desertion.
(Clarification; The German command structure for units behind the front is rather confusing, but Feldgendarme (both Wehrmacht and SS) could be under the command of either the Wehrmacht or the Waffen-SS near the front, but then come under the local SS occupation leader (HSSPF) etc. The "Feldjäger-Kommandos" were AFAIK directly under Wehrmacht control (OKW).)

So just being on the wrong road behind the lines without explicit orders could mean instant execution. I have seen an example where a group of German Staff officers simply was dragged out of their car and shot by Feldgendarme because they were driving in the wrong direction on the wrong road.

In short, special units was deployed against stragglers and deserters behind the frontline, and death by shooting or perhaps hanging, was more or less the default option when caught late in the war.

Another challenge was lack of papers (Ausweiss etc) that would allow you move in the hinterland, or even obtaining food. So you would have to either steal, plunder or rely on the mercy of others to obtain food, and since food was rationed, there usually wasn't much to give out either.

As for civilians: well, don't forget that a large amount of German civilians was very pro-Nazi, Pro-Hitler, and would not hesitate for a second to turn you in for desertion. Even non-Nazis could denounce you because they saw it as a duty to fight on, or simply because they really didn't like the idea about an armed deserter loitering in their neighbourhood.

So it would take certain, rare circumstances in order for a civilian to take you in as a deserter and hide you from authorities.

(Edit; clarification)