There is no such thing as “innocent” crossing of a border other than by authorized crossing points.
If done in large numbers, it is no longer a “refugee” situation, it is an invasion, and every nation has as some part of its legal code, a restriction on illegal border crossings.
It used to be, that on the border between the Soviet Union and Turkey, the Soviets would go on their side of the border (which had rather flimsy fencing), and plow the earth, leaving a surface on which footprints could be easily identified. Those intent on escaping the Soviet Union would walk backwards across this freshly plowed earth, giving the impression they were escaping Turkey to enter the Soviet Union.
Worked for a while, until the Russians finally caught on to how they were being pranked. Then they started building a better boundary fence, and manning it regularly.
Back when ‘Polish jokes’ were in vogue, one of the more memorable ones was...
Q
“How did the Germans invade Poland so easy in 1939”?
A
“They marched in backwards and EVERYONE thought they were leaving”.
Won’t get in any more ‘trouble’ for two .. SO here it is
Q
“Why won’t an Olympics be held in Poland”?
A
“Going by the standard of home country getting ‘1st shot’ at tickets, would mean that most everyone would be sitting behind a Pole”.