https://bbpress.org/forums/topic/allow-participants-to-trash-own-topics-and-posts/

bbp-allow-particiants-to-delete-their-own-posts.php

<?php
/*
Plugin Name: bbPress - Add delete_posts to partipant role
Plugin URI: https://bbpress.org/forums/topic/allow-participants-to-trash-own-topics-and-posts/
Description: 
Version: 
Author: 
Author URI: 
License: 
License URI: 
*/

/*Customize the BBPress roles to allow Participants to trash topics*/
add_filter( 'bbp_get_caps_for_role', 'ST_add_role_caps_filter', 10, 2 );

function ST_add_role_caps_filter( $caps, $role ){
    // Only filter for roles we are interested in!
    if( $role == 'bbp_participant' ) {

	$new_caps = array(
                // Primary caps
                'spectate'              => true,
                'participate'           => true,
                'moderate'              => false,
                'throttle'              => false,
                'view_trash'            => false,

                // Forum caps
                'publish_forums'        => false,
                'edit_forums'           => false,
                'edit_others_forums'    => false,
                'delete_forums'         => false,
                'delete_others_forums'  => false,
                'read_private_forums'   => false,
                'read_hidden_forums'    => false,

                // Topic caps
                'publish_topics'        => true,
                'edit_topics'           => true,
                'edit_others_topics'    => false,
                'delete_topics'         => true,
                'delete_others_topics'  => false,
                'read_private_topics'   => false,

                // Reply caps
                'publish_replies'       => true,
                'edit_replies'          => true,
                'edit_others_replies'   => false,
                'delete_replies'        => true,
                'delete_others_replies' => false,
                'read_private_replies'  => false,

                // Topic tag caps
                'manage_topic_tags'     => false,
                'edit_topic_tags'       => false,
                'delete_topic_tags'     => false,
                'assign_topic_tags'     => true,
            );	

	}

    return $new_caps;
}
/*Fixes an issue that only allows mods to trash topics.
bbpress.trac.wordpress.org/changeset/5852
bbpress.trac.wordpress.org/ticket/2685*/

add_filter( 'bbp_map_reply_meta_caps', 'ST_tweak_trash_meta_caps', 11, 4 );
add_filter( 'bbp_map_topic_meta_caps', 'ST_tweak_trash_meta_caps', 11, 4 );

// tweak for replies
function ST_tweak_trash_meta_caps( $caps, $cap, $user_id, $args ){

	// apply only to delete_reply and delete_topic
	if ( $cap == "delete_reply" || $cap == "delete_topic" ){
		// Get the post
		$_post = get_post( $args[0] );
		if ( !empty( $_post ) ) {

			// Get caps for post type object
			$post_type = get_post_type_object( $_post->post_type );
			$caps      = array();

			// Add 'do_not_allow' cap if user is spam or deleted
			if ( bbp_is_user_inactive( $user_id ) ) {
				$caps[] = 'do_not_allow';

			// Moderators can always edit forum content
			} elseif ( user_can( $user_id, 'moderate' ) ) {
				$caps[] = 'moderate';

			// User is author so allow edit if not in admin
            } elseif ( ! is_admin() && ( (int) $user_id === (int) $_post->post_author ) ) {
                $caps[] = $post_type->cap->delete_posts;

			// Unknown so map to delete_others_posts
			} else {
				$caps[] = $post_type->cap->delete_others_posts;
			}
		}

	}
	// return the capabilities
	return $caps;
}