We will achieve this functionality through EventObserver.

Here, I have used the event which is called

“controller_action_catalog_product_save_entity_after”

Step 1: Create event.xml in /etc/adminhtml folder in your module.

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Event/etc/events.xsd">
    <event name="controller_action_catalog_product_save_entity_after">
        <observer name="magemonkeys_saveproductlogic" instance="MagemonkeysSaveproductlogicObserverSaveProduct" />
    </event>
</config>

Step 2: Create a SaveProduct.php Observer in Observer Folder.

<?php
namespace MagemonkeysSaveproductlogicObserver;

use MagentoFrameworkEventObserverInterface;

class SaveProduct implements ObserverInterface
{
    protected $catalogData;

    protected $_resource;

    
    public function __construct(
        MagentoFrameworkAppResourceConnection $resource
        )
    {
        $this->_resource = $resource;
    }

    
    public function execute(MagentoFrameworkEventObserver $observer)
    {
        $connection = $this->_resource->getConnection();
        $table_name = $this->_resource->getTableName('product_oem');
        $productController = $observer->getController();
        $data = $productController->getRequest()->getPostValue();

        $mainProduct = $observer->getProduct();
        $productId = $mainProduct->getId();
        /* You can use you logic here */

        if(isset($data['product']['product_oem']) && $productId){
            $connection->query('DELETE FROM ' . $table_name . ' WHERE product_id =  ' . (int)$productId . ' ');
            $productOems = $data['product']['product_oem'];
            if(!is_array($productOems)){
                $productOems = array();
                $productOems[] = (int)$data['product']['product_oem'];
            }
            foreach ($productOems as $k => $v) {
                $connection->query('INSERT INTO ' . $table_name . ' VALUES ( ' . $v . ', ' . (int)$productId . ',0)');
            }
        }
    }
}
?>

After creating the above module, please run the upgrade, compile and static:content:deploy command to implement this module.