Dried blood spot (DBS) technology has become a promising utility for the transportation and storage of biological fluids aimed for the subsequent clinical analysis. The basis of the DBS method is the adsorption of the components of a biological sample onto the surface of a membrane carrier, followed by drying. After drying, the molecular components of the biosample (nucleic acids, proteins, and metabolites) can be analyzed using modern omics, immunological, or genomic methods. In this work, we investigated the safety of proteins on a membrane carrier by tryptic components over time and at different temperatures (+4, 0, 25 °C) and storage (0, 7, 14, and 35 days). It was shown that the choice of a protocol for preliminary sample preparation for subsequent analytical molecular measurements affects the quality of the experimental results. The protocol for preliminary preparation of a biosample directly in a membrane carrier is preferable compared to the protocol with an additional stage of elution of molecular components before the sample preparation procedures. It was revealed that the composition of biosamples remains stable at a temperature of −20 and +4 °C for 35 days of storage, and at +25 °C for 14 days.