This varies wildly between companies. I will provide you a somewhat traditional flow, but this will be limited due to lack of graphics.
First, you need to assume that there *may* be a separate Engineering BOM and Manufacturing BOM. For example, there may be differences in structuring (assembly levels), and some companies load their burdened labor costs into the Manufacturing BOM in order to account for the labor involved.
Next, understand that entire courses are taught on "Configuration Management". That's not a trivial topic.
I will also assume that a Change Control Board exists that represents all of the affected groups who have a dog in the fight -- Engineering, Manufacturing, Quality / R&T, Marketing, Sales, Purchasing, Regulatory Engineering (may be a separate group), Documentation, Tech Support -- everyone. Each company has its own policies as to makeup of this group, and who has signature authority within that group.
I'll break this into two sections -- initial product design and release, and post-release support.
1) In design, Engineering creates the Engineering BOM for the product. This document will specify each assembly and its components. The assembly structure is often reflected in an "indented" BOM. If the normal production purchasing means are used to procure prototype parts, the Engineering BOM, along with associated drawings, will be used to procure those parts. All of this is usually documented as part of an ECN (Engineering Change Notification) package.
2) After prototyping, Engineering will have a better idea of what's what, and *may* choose to try to release certain long lead piece part drawings for production purchase in order to meet the launch schedule. These should be "high confidence" parts, especially if they'll have to be tooled. These may or may not be a bit "out of the cycle" in that final vendors may not yet have been selected.
3) Apart from items in #2, and as subsystems and subassemblies are completed, drawing packages should be submitted to the CCB for approval. Adequate time must be given for document review, cost analysis, and perhaps even QA review of vendors. Design feature, cost and schedule goals are used for evaluation. If all of the CCB members with signature authority approve the package, it is sent to Purchasing for procurement. Concurrently, the BOM and its associated drawings are locked in as a "stake in the ground" and the design as approved becomes the "design of record", and is typically entered into "the system" by whatever means the company uses to store and control its documentation and record its BOM. In a good system, that BOM will now be used to generate an MRP that will provide Purchasing with scheduled quantities of parts that must be ordered to meet the manufacturing schedule, all based upon the lead time of the individual parts.
At this point, NO changes to the drawings or BOM should occur outside of the approval process, assuring that everyone is always on the same page. This also establishes the base configuration of the product, although that may still change prior to production.
The final information is provided electronically these days, made available to all of the CCB signatories.
Most companies will provide for both the "normal" ECN (Engineering Change Notification) process and some sort of "emergency" method for making changes. It's not atypical to see something like a TDA (Temporary Deviation Authorization) process put into place that allows on-the-fly changes to respond to the realities of getting a product manufactured. The TDA should not be used for changes that will be made permanent unless time simply does not permit the creation of "clean" drawings and the associated ECN to release them. Where the change will be permanent, the associated ECN should be expedited and the TDA cancelled with the release of the ECN.
TDA's may cause variations from the original BOM as well as the individual part drawings. It could be that a vendor has supplied a part that, while not per the drawing, is acceptable for production. Or perhaps the vendor has identified something amiss with the drawing that requires correction -- thankfully, it's much harder to create some errors than it used ot be (e.g., dimensional errors).
4) Once the package is released and under ECN control, changes are a function of ECN and the CCB. Different companies allow different groups to initiate a change request via ECR (Engineering Change Request) -- those are reviewed and feedback provided from Engineering to the group/person authoring the ECR. These can be discussed by the CCB or left in the hands of Engineering to accept or reject.
5) In response to an ECR, if a change will be made, the process of documenting parts and BOM changes is as it was in the creation of the original. If accepted by the CCB, the information (drawings, BOM, etc.) are circulated as is the case during release, and "documents" (likely electronic, these days) are distributed and controlled in the same way as well.
6) Configuration management is a science unto itself. Trying to coordinate cut-ins by date or serial number and understanding what was shipped is a process that comes in many forms. Issues of the compatibility of new/old parts and assemblies must be understood and documented, and careful records kept where it makes sense. This is a problem in many companies that aren't doing "volume" production or are doing "one off" work -- they tend to ignore this step in the process, and are unable to point to a BOM that accurately defines what went out the door.
GENERAL RULE: You should be able to create a stack of documents (paper or electronic) at any time that represents the product that was shipped.
Well, that's a real thumbnail sketch of what a process might look like. There are nearly as many specific process descriptions for this as there are companies. I've left out a bunch of the detail and nuance, since it would take PAGES to define. I would suggest that, if you are able, you find a company that does this well and is willing to share a copy of their own process from design to shipment of a new product.