Is the B cell receptor still expressed on a B cell once it has begun to produce soluble antibodies? Is there a gene change that prevents the membrane-bound form from being produced anymore?
B cells can secrete antibody before they are terminally differentiated into plasma cells, so there is a phase during which both membrane-bound and secretory antibodies can be produced by the same cell:
When a naïve or memory B cell is activated by antigen (with the aid of a helper T cell), it proliferates and differentiates into an antibody-secreting effector cell. Such cells make and secrete large amounts of soluble (rather than membrane-bound) antibody, which has the same unique antigen-binding site as the cell-surface antibody that served earlier as the antigen receptor (Figure 24-17). Effector B cells can begin secreting antibody while they are still small lymphocytes, but the end stage of their maturation pathway is a large plasma cell
Plasma cells, generally speaking, have little or no surface immunoglobulin, but it's been claimed that some subsets of plasma cells do have surface Ig:
Surprisingly, although IgG PCs downregulated surface IgG expression, IgA and IgM PCs expressed their respective isotype both intracellularly and on the plasma membrane (Figure 1A, lower panel). Importantly, concordant Ig’s were also detected on the plasma membrane of IgA and IgM, but not IgG, PCs isolated from BM or colon LP indicating that this property is a characteristic of PCs present in their physiological niches
Once B cell starts secreting soluble antibodies, it is no longer a B cell, it is called a plasma cell hence normal B cells do not secrete soluble antibodies before becoming plasma cells. It is the BCR that is secreted. B cells can either differentiate into memory or plasma cells. Plasma cells produce soluble antibody molecules closely modeled after the receptors of the precursor B cell. The plasma cell continuously produces soluble antibodies. I hope this helps since I did not directly answer your questions because they were based on inaccurate information/bases. Please let me know if any other questions based on the information I provided