Can Euchromatin convert into Heterochromatin?

I would suggest in the future doing a small amount of research before asking. For example, the wikipedia page for euchromatin says this:

Euchromatin participates in the active transcription of DNA to mRNA products. The unfolded structure allows gene regulatory proteins and RNA polymerase complexes to bind to the DNA sequence, which can then initiate the transcription process. Not all euchromatin is necessarily transcribed, but in general that which is not is transformed into heterochromatin to protect the genes while they are not in use. There is therefore a direct link to how actively productive a cell is and the amount of euchromatin that can be found in its nucleus. It is thought that the cell uses transformation from euchromatin into heterochromatin as a method of controlling gene expression and replication, since such processes behave differently on densely compacted chromatin, known as the 'accessibility hypothesis'. One example of constitutive euchromatin that is 'always turned on' is housekeeping genes, which code for the proteins needed for basic functions of cell survival.

Facultative heterochromatin is chromatin which converts back and forth depending on circumstances. This occurs through (de)"condensation" or (de)"compaction" of chromatin:

Among the molecular components that appear to regulate the spreading of heterochromatin are the Polycomb-group proteins and non-coding genes such as Xist. The mechanism for such spreading is still a matter of controversy.[19] The polycomb repressive complexes PRC1 and PRC2 regulate chromatin compaction and gene expression and have a fundamental role in developmental processes.

I would suggest reading those pages a little bit and coming up with a more specific question if they don't answer it.