Say that I have vendors selling various products. So, at a basic level, I will have the following tables: vendor, product, vendor_product
You already suggested a vendor, product and vendor_product mapping table. You want vendors to share the same product if they both want to use it, but you don't want duplicate products. Right?
If so, then define a unique index/constraint on the natural key that identifies a product (product name?).
If a vendor adds a product, and it doesn't exist, insert it into the product table, and map it to that vendor via the vendor_product table.
If the product already exists, but is mapped to another vendor, do not insert anything into the product table, and add another mapping row mapping the new vendor to the existing product (so that now the product is mapped to two vendors).
Finally, when a vendor removes a product, instead of actually removing it, just delete the vendor_product reference mapping the two. Finally, if no other vendors are still referencing a product, you can remove the product. Alternatively, you could run a script periodically that deletes all products that no longer have vendors referencing them.
Finally, have a flag on the product table that says that you've reviewed the product, and then use something like this to query for products viewable by a given vendor (we'll say vendor id 7):
select product.*
from product
left join vendor_map
on vendor_map.product_id = product.product_id
where vendor_map.vendor_id = 7
or product.reviewed = 1;
Finally, if a product is owned by multiple vendors, then you can either disallow edits or perhaps "split" the single product into a new unique product when one of the owning vendors tries to edit it, and allow them to edit their own copy of the product. They would likely need to modify the product name though, unless you come up with some other natural key to base your unique constraint on.