Why is protein cyclisation desirable?

As described in the abstract of Synthetic Cross-linking of Peptides: Molecular Linchpins for Peptide Cyclization by Derda et al., protein cyclization improves:

resistance to proteolytic degradation and conformational stability. The latter property leads to an increase in binding potency and increased bioavailability due to increased permeation through biological membranes.

In simpler terms, a protein that is cyclized is less likely to:

1. Fold into an unhelpful shape.
2. Be broken up by an enzyme.

Thus, they are more likely to:

1. Act as better binders for a given target
2. Make it across a cell membrane