<input type="text" name="input_value" id="input_value" />

<script>
    require(['jquery'], function($) {
        $(document).ready(function() {
            $('#input_value').on('change', function() {
                var inputValue = $(this).val();
                $.ajax({
                    url: '<?php echo $block->getUrl("module/controller/action"); ?>',
                    type: 'POST',
                    data: {input_value: inputValue},
                    success: function(response) {
                        // 处理响应
                    }
                });
            });
        });
    });
</script>

<?php
namespace Vendor\Module\Controller\ControllerName;

class ActionName extends \Magento\Framework\App\Action\Action
{
    protected $resultPageFactory;

    public function __construct(
        \Magento\Framework\App\Action\Context $context,
        \Magento\Framework\View\Result\PageFactory $resultPageFactory
    ) {
        $this->resultPageFactory = $resultPageFactory;
        parent::__construct($context);
    }

    public function execute()
    {
        $inputValue = $this->getRequest()->getParam('input_value');
        $block = $this->_view->getLayout()->getBlock('block_name');
        $block->setData('input_value', $inputValue);
        return $this->resultPageFactory->create();
    }
}

<?php
namespace Vendor\Module\Block;

class BlockName extends \Magento\Framework\View\Element\Template
{
    protected $inputValue;

    public function setInputValue($inputValue)
    {
        $this->inputValue = $inputValue;
    }

    public function getInputValue()
    {
        return $this->inputValue;
    }
}