Can Inductor force abrupt current change through another inductor?
In real world there is always some resistance. At worst it is resistance through air, or through the PCB substrate, across either inductor or across the switch back to the source. (Most likely inside the switch.)

Since that resistance is very large, the voltage induced across it is very large also and in this instance is negative. If it is through the air, the voltage is large enough to ionize the air and an arc, spark, will form. 

Since R is large the current decays very very quickly, meanwhile the current in the second inductor will also grows quickly till the point where the arc extinguishes.