If this is only due to the breakage of hydrogen bonds by increasing ioninc strength of the solution than please explain why hydrogens bonds break in such a solution
Also add another explanation for the same (if any)
The question is why the fibroin dissolve in water when Li+ and Br- are present. The H-bond breakage may be induced by strong H-bond acceptor (HBA, basic) solvents, which are known to dissolve cellulose and silk. So Br- may be involved as a HBA ion by coordination to H-bond donors in silk. In this case, other bromides (Na+, K+, NH4+, etc.) may work too? With my knowledge of Li+ interactions, I suppose that this cation cooperates also as a Lewis acid, and help solvation in water by adduct formation on basic parts (of amide C=O in particular). A good review where the effets of salts are described:
Russian Journal of Applied Chemistry, 2006, Vol. 79, No. 6, pp. 869-876
Structure and Solubility of Natural Silk Fibroin