How to search id from one table in another table's nvarchar column
Yes, you can use % with LIKE. Since you are converting the INT "id" into a string, you can then concatenate the % character on both sides. But you also need to include a space separating each of them from the converted "id" so that you don't have an "id" of 23 matching a parameters value of something like "abc 1234 def". And yes, you can JOIN the tables since that is just a different way of expressing the same thing that you are already attempting.

SETUP

-- DROP TABLE #table1;
CREATE TABLE #table1 ( [id] INT NOT NULL PRIMARY KEY, [name] NVARCHAR(30));
-- DROP TABLE #table2;
CREATE TABLE #table2 ( [pid] INT NOT NULL PRIMARY KEY, [parameters] NVARCHAR(500));

SET NOCOUNT ON;
INSERT INTO #table1 ([id], [name]) VALUES (1, N'a');
INSERT INTO #table1 ([id], [name]) VALUES (2, N'b');
INSERT INTO #table1 ([id], [name]) VALUES (3, N'c');
INSERT INTO #table1 ([id], [name]) VALUES (12, N'ab');
INSERT INTO #table1 ([id], [name]) VALUES (23, N'bc');
INSERT INTO #table1 ([id], [name]) VALUES (123, N'abc');


INSERT INTO #table2 ([pid], [parameters]) VALUES (1, N'some text 12345 some text');
INSERT INTO #table2 ([pid], [parameters]) VALUES (2, N'DD 2 DD');
INSERT INTO #table2 ([pid], [parameters]) VALUES (3, N'EEE EE 123 EEEEE');
INSERT INTO #table2 ([pid], [parameters]) VALUES (4, N'NO23 12NO');
INSERT INTO #table2 ([pid], [parameters]) VALUES (5, N'HHHHHH YYY 23 ZZZZZ');
INSERT INTO #table2 ([pid], [parameters]) VALUES (6, N'QQQQQ r2q RRRRR');


CORRELATED SUBQUERY

SELECT r.[id], r.[name]
FROM #table1 r
WHERE EXISTS
(
  SELECT *
  FROM #table2 tmp
  WHERE tmp.[parameters] LIKE N'% ' + CONVERT(NVARCHAR(15), r.[id]) + N' %'
);
/*
id     name
2      b
23     bc
123    abc
*/


JOIN

SELECT t1.[id], t1.[name], t2.[pid]
FROM #table1 t1
INNER JOIN #table2 t2
        ON t2.[parameters] LIKE N'% ' + CONVERT(NVARCHAR(15), t1.[id]) + N' %';
/*
id     name    pid
2      b       2
23     bc      5
123    abc     3
*/