  Many technological applications of multiferroics are based on their ability
to reconstruct the domain structure (DS) under the action of small external
fields. In the present paper we analyze the different scenarios of the DS
behavior in a multiferroic that shows simultaneously ferro- and
antiferromagnetic ordering on the different systems of magnetic ions. We
consider the way to control a composition of the DS and macroscopic properties
of the sample by an appropriate field treatment. We found out that sensitivity
of the DS to the external magnetic field and the magnetic susceptibility in a
low-field region are determined mainly by the destressing effects (that have
magnetoelastic origin). In a particular case of Sr$_{2}$Cu$_{3}$O$_{4}$Cl$_{2}$
crystal we anticipate the peculiarities of the elastic and magnetoelastic
properties at $T\approx 100$ K.
